Finite Group Databasebeta

← Group #72222812

Character table — Group #72222812

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size11222224444488882244444888881616161633666661212121212242424242244444888881616161644888881616161616323232326612121212122424242424484848483366666121212121224242424661212121212242424242448484848991818181818363636363672727272
order1224488816161616244436612122424244848484861212122224488816161616244436612122424244848484861212123661212242424484848486121212666121224242448484848612121222244888161616162444666121224242448484848612121222244888161616162444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1
χ311111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-1
χ411111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ511-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i
χ611-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii
χ711-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii
χ811-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i
χ922222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-200000000
χ10222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000
χ11222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000
χ1222-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i20000
χ1322-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i20000
χ1422-2-2222-20000000022-2-2222-20000000022-2-2222-20000000022-2-2222-20000000022-2-2222-20000000022-2-2222-20000000022-2-2222-20000000022-2-2222-20000000022-2-2222-200000000
χ154-40002i2−2i20000000004-40002i2−2i20000000004-40002i2−2i20000000004-40002i2−2i20000000004-40002i2−2i20000000004-40002i2−2i20000000004-40002i2−2i20000000004-40002i2−2i20000000004-40002i2−2i2000000000
χ164-4000−2i22i20000000004-4000−2i22i20000000004-4000−2i22i20000000004-4000−2i22i20000000004-4000−2i22i20000000004-4000−2i22i20000000004-4000−2i22i20000000004-4000−2i22i20000000004-4000−2i22i2000000000
χ1711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ18111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1911111111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ2011111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1
χ2111-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i-1-111-111-1−i−iii-11−ii11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i-1-111-111-1−i−iii-11−ii11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i-1-111-111-1−i−iii-11−ii
χ2211-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii-1-111-111-1−i−iii1-1i−i11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii-1-111-111-1−i−iii1-1i−i11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii-1-111-111-1−i−iii1-1i−i
χ2311-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii-1-111-111-1ii−i−i-11i−i11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii-1-111-111-1ii−i−i-11i−i11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii-1-111-111-1ii−i−i-11i−i
χ2411-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i-1-111-111-1ii−i−i1-1−ii11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i-1-111-111-1ii−i−i1-1−ii11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i-1-111-111-1ii−i−i1-1−ii
χ2522222-2-2-20000000022222-2-2-200000000-2-2-2-2-22220000000022222-2-2-20000000022222-2-2-200000000-2-2-2-2-22220000000022222-2-2-20000000022222-2-2-200000000-2-2-2-2-222200000000
χ26222-2-20002−22−20000222-2-20002−22−20000-2-2-222000−22−220000222-2-20002−22−20000222-2-20002−22−20000-2-2-222000−22−220000222-2-20002−22−20000222-2-20002−22−20000-2-2-222000−22−220000
χ27222-2-2000−22−220000222-2-2000−22−220000-2-2-2220002−22−20000222-2-2000−22−220000222-2-2000−22−220000-2-2-2220002−22−20000222-2-2000−22−220000222-2-2000−22−220000-2-2-2220002−22−20000
χ2822-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i20000-2-22-22000−i2i2i2−i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i20000-2-22-22000−i2i2i2−i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i20000-2-22-22000−i2i2i2−i20000
χ2922-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i20000-2-22-22000i2−i2−i2i2000022-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i20000-2-22-22000i2−i2−i2i2000022-22-2000−i2i2i2−i2000022-22-2000−i2i2i2−i20000-2-22-22000i2−i2−i2i20000
χ3022-2-2222-20000000022-2-2222-200000000-2-222-2-2-220000000022-2-2222-20000000022-2-2222-200000000-2-222-2-2-220000000022-2-2222-20000000022-2-2222-200000000-2-222-2-2-2200000000
χ314-40002i2−2i20000000004-40002i2−2i2000000000-44000−2i22i20000000004-40002i2−2i20000000004-40002i2−2i2000000000-44000−2i22i20000000004-40002i2−2i20000000004-40002i2−2i2000000000-44000−2i22i2000000000
χ324-4000−2i22i20000000004-4000−2i22i2000000000-440002i2−2i20000000004-4000−2i22i20000000004-4000−2i22i2000000000-440002i2−2i20000000004-4000−2i22i20000000004-4000−2i22i2000000000-440002i2−2i2000000000
χ332222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ34222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ3522222222-2-2-2-222-2-2-1-1-1-1-1-1-1-11111-1-111000000000000000022222222-2-2-2-222-2-2-1-1-1-1-1-1-1-11111-1-111000000000000000022222222-2-2-2-222-2-2-1-1-1-1-1-1-1-11111-1-1110000000000000000
χ3622222222-2-2-2-2-2-222-1-1-1-1-1-1-1-1111111-1-1000000000000000022222222-2-2-2-2-2-222-1-1-1-1-1-1-1-1111111-1-1000000000000000022222222-2-2-2-2-2-222-1-1-1-1-1-1-1-1111111-1-10000000000000000
χ3722-2-22-2-222i2i−2i−2i2-22i−2i-1-111-111-1−i−iii-11−ii000000000000000022-2-22-2-222i2i−2i−2i2-22i−2i-1-111-111-1−i−iii-11−ii000000000000000022-2-22-2-222i2i−2i−2i2-22i−2i-1-111-111-1−i−iii-11−ii0000000000000000
χ3822-2-22-2-222i2i−2i−2i-22−2i2i-1-111-111-1−i−iii1-1i−i000000000000000022-2-22-2-222i2i−2i−2i-22−2i2i-1-111-111-1−i−iii1-1i−i000000000000000022-2-22-2-222i2i−2i−2i-22−2i2i-1-111-111-1−i−iii1-1i−i0000000000000000
χ3922-2-22-2-22−2i−2i2i2i2-2−2i2i-1-111-111-1ii−i−i-11i−i000000000000000022-2-22-2-22−2i−2i2i2i2-2−2i2i-1-111-111-1ii−i−i-11i−i000000000000000022-2-22-2-22−2i−2i2i2i2-2−2i2i-1-111-111-1ii−i−i-11i−i0000000000000000
χ4022-2-22-2-22−2i−2i2i2i-222i−2i-1-111-111-1ii−i−i1-1−ii000000000000000022-2-22-2-22−2i−2i2i2i-222i−2i-1-111-111-1ii−i−i1-1−ii000000000000000022-2-22-2-22−2i−2i2i2i-222i−2i-1-111-111-1ii−i−i1-1−ii0000000000000000
χ4144444-4-4-400000000-2-2-2-2-222200000000000000000000000044444-4-4-400000000-2-2-2-2-222200000000000000000000000044444-4-4-400000000-2-2-2-2-2222000000000000000000000000
χ42444-4-400022−2222−220000-2-2-222000−22−2200000000000000000000444-4-400022−2222−220000-2-2-222000−22−2200000000000000000000444-4-400022−2222−220000-2-2-222000−22−2200000000000000000000
χ43444-4-4000−2222−22220000-2-2-2220002−22−200000000000000000000444-4-4000−2222−22220000-2-2-2220002−22−200000000000000000000444-4-4000−2222−22220000-2-2-2220002−22−200000000000000000000
χ4444-44-40002i2−2i2−2i22i20000-2-22-22000−i2i2i2−i20000000000000000000044-44-40002i2−2i2−2i22i20000-2-22-22000−i2i2i2−i20000000000000000000044-44-40002i2−2i2−2i22i20000-2-22-22000−i2i2i2−i200000000000000000000
χ4544-44-4000−2i22i22i2−2i20000-2-22-22000i2−i2−i2i20000000000000000000044-44-4000−2i22i22i2−2i20000-2-22-22000i2−i2−i2i20000000000000000000044-44-4000−2i22i22i2−2i20000-2-22-22000i2−i2−i2i200000000000000000000
χ4644-4-4444-400000000-2-222-2-2-2200000000000000000000000044-4-4444-400000000-2-222-2-2-2200000000000000000000000044-4-4444-400000000-2-222-2-2-22000000000000000000000000
χ478-80004i2−4i2000000000-44000−2i22i200000000000000000000000008-80004i2−4i2000000000-44000−2i22i200000000000000000000000008-80004i2−4i2000000000-44000−2i22i20000000000000000000000000
χ488-8000−4i24i2000000000-440002i2−2i200000000000000000000000008-8000−4i24i2000000000-440002i2−2i200000000000000000000000008-8000−4i24i2000000000-440002i2−2i20000000000000000000000000
χ49111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ50111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111
χ5211111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ5311-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i11-1-11-1-11ii−i−i1-1i−i-1-111-111-1−i−iii-11−ii-1-111-111-1−i−iii-11−ii-1-111-111-1−i−iii-11−ii
χ5411-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii11-1-11-1-11ii−i−i-11−ii-1-111-111-1−i−iii1-1i−i-1-111-111-1−i−iii1-1i−i-1-111-111-1−i−iii1-1i−i
χ5511-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii11-1-11-1-11−i−iii1-1−ii-1-111-111-1ii−i−i-11i−i-1-111-111-1ii−i−i-11i−i-1-111-111-1ii−i−i-11i−i
χ5611-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i11-1-11-1-11−i−iii-11i−i-1-111-111-1ii−i−i1-1−ii-1-111-111-1ii−i−i1-1−ii-1-111-111-1ii−i−i1-1−ii
χ5722222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-200000000-2-2-2-2-222200000000-2-2-2-2-222200000000-2-2-2-2-222200000000
χ58222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000222-2-20002−22−20000-2-2-222000−22−220000-2-2-222000−22−220000-2-2-222000−22−220000
χ59222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000222-2-2000−22−220000-2-2-2220002−22−20000-2-2-2220002−22−20000-2-2-2220002−22−20000
χ6022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i2000022-22-2000i2−i2−i2i20000-2-22-22000−i2i2i2−i20000-2-22-22000−i2i2i2−i20000-2-22-22000−i2i2i2−i20000
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χ13644-4-44-4-44−4i−4i4i4i-444i−4i-2-222-222-22i2i−2i−2i2-2−2i2i0000000000000000-2-222-222-22i2i−2i−2i2-2−2i2i11-1-11-1-11−i−iii-11i−i0000000000000000000000000000000000000000000000000000000000000000
χ13788888-8-8-800000000-4-4-4-4-4444000000000000000000000000-4-4-4-4-44440000000022222-2-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ138888-8-800042−4242−420000-4-4-444000−2222−222200000000000000000000-4-4-444000−2222−22220000222-2-20002−22−200000000000000000000000000000000000000000000000000000000000000000000
χ139888-8-8000−4242−42420000-4-4-44400022−2222−2200000000000000000000-4-4-44400022−2222−220000222-2-2000−22−2200000000000000000000000000000000000000000000000000000000000000000000
χ14088-88-80004i2−4i2−4i24i20000-4-44-44000−2i22i22i2−2i200000000000000000000-4-44-44000−2i22i22i2−2i2000022-22-2000i2−i2−i2i200000000000000000000000000000000000000000000000000000000000000000000
χ14188-88-8000−4i24i24i2−4i20000-4-44-440002i2−2i2−2i22i200000000000000000000-4-44-440002i2−2i2−2i22i2000022-22-2000−i2i2i2−i200000000000000000000000000000000000000000000000000000000000000000000
χ14288-8-8888-800000000-4-444-4-4-44000000000000000000000000-4-444-4-4-440000000022-2-2222-2000000000000000000000000000000000000000000000000000000000000000000000000
χ14316-160008i2−8i2000000000-88000−4i24i20000000000000000000000000-88000−4i24i20000000004-40002i2−2i20000000000000000000000000000000000000000000000000000000000000000000000000
χ14416-16000−8i28i2000000000-880004i2−4i20000000000000000000000000-880004i2−4i20000000004-4000−2i22i20000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).