Finite Group Databasebeta

← Group #10693486

Character table — Group #10693486

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111111111111222222222222222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444424242424242424242424242424242424
order122222224444444434444444466666661212121212121212121212121212121212121212121212128888888888888888888888882424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424244444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111−i−iiiii−i−i
χ1211111111-1-1-1-1-1-1-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1ii−i−i−i−iii
χ1311111111-1-1-1-1-1-1-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111ii−i−i−i−iii
χ1611111111-1-1-1-1-1-1-1-1111-1-111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1−i−iiiii−i−i
χ1722222222222222222-2-2-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000002222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111110000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111112222-2-2-2-20000000000000000-1-1-1-11111-1-1-1-111113333−3−3−3−33333−3−3−3−33333−3−3−3−33333−3−3−3−30000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111112222-2-2-2-20000000000000000-1-1-1-11111-1-1-1-11111−3−3−3−33333−3−3−3−33333−3−3−3−33333−3−3−3−333330000000000000000
χ252222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-2-2-2-2222200000000000000001111-1-1-1-11111-1-1-1-13333−3−3−3−33333−3−3−3−3−3−3−3−33333−3−3−3−333330000000000000000
χ262222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-2-2-2-2222200000000000000001111-1-1-1-11111-1-1-1-1−3−3−3−33333−3−3−3−333333333−3−3−3−33333−3−3−3−30000000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-222-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i00000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-222-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i0000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i2222-2-2-2-22i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000
χ3022222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i0000000000000000
χ3122222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111−2i−2i2i2i−2i−2i2i2i2222-2-2-2-2−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000
χ3222222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111−2i−2i2i2i−2i−2i2i2i-2-2-2-222222i2i2i2i−2i−2i−2i−2iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii0000000000000000
χ3322222222-2-2-2-2-2-2-2-2-1-2-222-2-222-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-12i2i−2i−2i−2i−2i2i2i0000000000000000−i−i−i−iiiiiiiii−i−i−i−i3333−3−3−3−3−3−3−3−33333i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000000000000000
χ3422222222-2-2-2-2-2-2-2-2-1-2-222-2-222-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-12i2i−2i−2i−2i−2i2i2i0000000000000000−i−i−i−iiiiiiiii−i−i−i−i−3−3−3−333333333−3−3−3−3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000000000000000
χ3522222222-2-2-2-2-2-2-2-2-1-2-222-2-222-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−2i−2i2i2i2i2i−2i−2i0000000000000000iiii−i−i−i−i−i−i−i−iiiii3333−3−3−3−3−3−3−3−33333−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000000000000000
χ3622222222-2-2-2-2-2-2-2-2-1-2-222-2-222-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−2i−2i2i2i2i2i−2i−2i0000000000000000iiii−i−i−i−i−i−i−i−iiiii−3−3−3−333333333−3−3−3−3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000000000000000
χ3722-2-22-22-22i−2i2i−2i2i−2i2i−2i20000000022-2-22-2-200002i2i−2i−2i000000002i2i−2i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2322−2−2−i2−i2i2i21−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2322−2−222−2−2−i2−i2i2i2−i2−i2i2i21−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000000000000000
χ3822-2-22-22-22i−2i2i−2i2i−2i2i−2i20000000022-2-22-2-200002i2i−2i−2i000000002i2i−2i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2−222i2i2−i2−i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2−222−2−222i2i2−i2−i2i2i2−i2−i2−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000000000000000
χ3922-2-22-22-22i−2i2i−2i2i−2i2i−2i20000000022-2-22-2-200002i2i−2i−2i000000002i2i−2i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2322−2−2−i2−i2i2i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2322−2−222−2−2−i2−i2i2i2−i2−i2i2i2−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000000000000000
χ4022-2-22-22-22i−2i2i−2i2i−2i2i−2i20000000022-2-22-2-200002i2i−2i−2i000000002i2i−2i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2−222i2i2−i2−i21−i1−i−1+i−1+i1+i1+i−1−i−1−i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2−222−2−222i2i2−i2−i2i2i2−i2−i21−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000000000000000
χ4122-2-22-22-22i−2i2i−2i2i−2i2i−2i-100000000-1-111-11133−3−3−i−iii−i3−i3i3i333−3−3−i−iii−i3−i3i3i30000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2322−2−2−i2−i2i2i21−i1−i−1+i−1+i1+i1+i−1−i−1−i−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ20−ζ22−ζ20−ζ22ζ20+ζ22ζ20+ζ22−ζ4−ζ14−ζ4−ζ14ζ4+ζ14ζ4+ζ14−ζ4+ζ14−ζ4+ζ14ζ4−ζ14ζ4−ζ14−ζ20+ζ22−ζ20+ζ22ζ20−ζ22ζ20−ζ220000000000000000
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χ4322-2-22-22-22i−2i2i−2i2i−2i2i−2i-100000000-1-111-11133−3−3−i−iii−i3−i3i3i333−3−3−i−iii−i3−i3i3i300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2322−2−2−i2−i2i2i2−1+i−1+i1−i1−i−1−i−1−i1+i1+iζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ20+ζ22ζ20+ζ22−ζ20−ζ22−ζ20−ζ22ζ4+ζ14ζ4+ζ14−ζ4−ζ14−ζ4−ζ14ζ4−ζ14ζ4−ζ14−ζ4+ζ14−ζ4+ζ14ζ20−ζ22ζ20−ζ22−ζ20+ζ22−ζ20+ζ220000000000000000
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χ1384-44-44-4-44−4i4i−4i4i4i−4i4i−4i-2-44−4i4i4-44i−4i2-22-22-222-22-22i−2i2i−2i2i−2i2i−2i-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1394-4-4444-4-44444-4-4-4-4400000000-444-4-4-4400004-4-4400000000-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1404-4-4444-4-44444-4-4-4-4-2000000002-2-2222-223−23−2323-222-223−23−2323−232323−232-2-22−232323−230000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1414-4-4444-4-44444-4-4-4-4-2000000002-2-2222-2−232323−23-222-2−232323−2323−23−23232-2-2223−23−23230000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1424-4-4444-4-4-4-4-4-44444400000000-444-4-4-440000-444-4000000004-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1434-4-4444-4-4-4-4-4-44444-2000000002-2-2222-223−23−23232-2-22−232323−23−232323−23-222-223−23−23230000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1444-4-4444-4-4-4-4-4-44444-2000000002-2-2222-2−232323−232-2-2223−23−232323−23−2323-222-2−232323−230000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.