Finite Group Databasebeta

← Group #72252311

Character table — Group #72252311

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150
size111122222222222222222244444444444444444444444444444444444444888888888888888888888888888888888888888888888888242424242424242436363636363636363636363648484848484848484848484848484848484848487272
order122222222233444466666634466666666666666666666666666612121212121212124444121212121212121212121212121212121212121212121212121212121212121212121212121212121212121222444444224444444444668888121212121212242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-11-11-11-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-11-11-11-11-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-11-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1-1-1-1-1111111111-1-1-11111-1-11-1-1-1-1-11111-1-1
χ7111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1-1-1-111111111-1111-1-1-1-111-111111-1-1-1-1-1-1
χ8111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111
χ9111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1ii−i−i11111111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1111-1-1-1-111-1-1iiii−i−i−i−i11i−ii−i1-11-1-1-1ii−i−iii−i−i-11
χ10111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1ii−i−i11111111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1-11-1-11-11-1-111−i−i−i−iiiii1-1i−i−ii1-1-11-11ii−i−i−i−iii1-1
χ11111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1ii−i−i11111111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-11-111-11-1-1-111−i−i−i−iiiii-11−iii−i-111-11-1−i−iiiii−i−i1-1
χ12111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1ii−i−i11111111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1111111-1-1iiii−i−i−i−i-1-1−ii−ii-11-1111−i−iii−i−iii-11
χ13111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1−i−iii11111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1111-1-1-1-111-1-1−i−i−i−iiiii11−ii−ii1-11-1-1-1−i−iii−i−iii-11
χ14111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1−i−iii11111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1-11-1-11-11-1-111iiii−i−i−i−i1-1−iii−i1-1-11-11−i−iiiii−i−i1-1
χ15111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1−i−iii11111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-11-111-11-1-1-111iiii−i−i−i−i-11i−i−ii-111-11-1ii−i−i−i−iii1-1
χ16111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1−i−iii11111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-1-1-1111111-1-1−i−i−i−iiiii-1-1i−ii−i-11-1111ii−i−iii−i−i-11
χ17222222222222-2-2-2-22222222-2-2222222222222222222222222222-2-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-200000000000000000000000000002-2
χ18222222222222-2-2-2-22222222-2-2222222222222222222222222222-2-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-2220000000000000000000000000000-22
χ1922222222222-1222222-1-12-1-12222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1020202020000000000000-1002200-1-10-10000-1-1-1-100
χ2022222222222-1222222-1-12-1-12222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10-20-20-20-20000000000000100-2-20011010000111100
χ2122222222222-1222222-1-12-1-12222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-2111111111111020202020000000000000-100-2-200-1-10-10000111100
χ2222222222222-1222222-1-12-1-12222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-21111111111110-20-20-20-20000000000000100220011010000-1-1-1-100
χ232222222222-122222-1-122-12-122-1-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1222222-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-120202020000000000000-102200-1-100-10-1-1-1-1000000
χ242222222222-122222-1-122-12-122-1-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1222222-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-20-20-20-2000000000000010-2-2001100101111000000
χ252222222222-122222-1-122-12-122-1-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-122-2-2-2-2-1-122-1-1-1-1-1-1-1-11111-2-2-2-2111111111111-2-2-2-21111111120202020000000000000-10-2-200-1-100-101111000000
χ262222222222-122222-1-122-12-122-1-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-122-2-2-2-2-1-122-1-1-1-1-1-1-1-11111-2-2-2-2111111111111-2-2-2-211111111-20-20-20-20000000000000102200110010-1-1-1-1000000
χ27222222-2-2-2-22222222222222-2-22222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22-2-2222222220000-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000022220000000000000000000000000000-2-2
χ28222222-2-2-2-22222222222222-2-22222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22-2-2222222220000-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000-2-2-2-2000000000000000000000000000022
χ29222222-2-2-2-22-1-2-2-2-222-1-12-1-12222-1-1-2-2-2111-1-1-1-1-1-1111111-21-111-2-211-2-2112i2i−2i−2i22-1-1-1-1-1-111112i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiiiiiii02020-20-20000000000000-1002i−2i00-11010000−i−iii00
χ30222222-2-2-2-22-1-2-2-2-222-1-12-1-12222-1-1-2-2-2111-1-1-1-1-1-1111111-21-111-2-211-2-2112i2i−2i−2i22-1-1-1-1-1-111112i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiiiiiii0-20-202020000000000000100−2i2i001-10-10000ii−i−i00
χ31222222-2-2-2-22-1-2-2-2-222-1-12-1-12222-1-1-2-2-2111-1-1-1-1-1-1111111-21-111-2-211-2-211−2i−2i2i2i22-1-1-1-1-1-11111−2i−2i−2i−2iiiiiiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i02020-20-20000000000000-100−2i2i00-11010000ii−i−i00
χ32222222-2-2-2-22-1-2-2-2-222-1-12-1-12222-1-1-2-2-2111-1-1-1-1-1-1111111-21-111-2-211-2-211−2i−2i2i2i22-1-1-1-1-1-11111−2i−2i−2i−2iiiiiiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i0-20-2020200000000000001002i−2i001-10-10000−i−iii00
χ33222222-2-2-2-2-12-2-2-2-2-1-122-12-122-1-122111-2-2-2-1-1-1-1-1-11111111-2-11111-2-211-2-22i2i−2i−2i-1-122-1-1-1-11111−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−iiiii−2i−2i−2i−2iiiiiiiii2020-20-20000000000000-102i−2i00-110010−i−iii000000
χ34222222-2-2-2-2-12-2-2-2-2-1-122-12-122-1-122111-2-2-2-1-1-1-1-1-11111111-2-11111-2-211-2-22i2i−2i−2i-1-122-1-1-1-11111−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−iiiii−2i−2i−2i−2iiiiiiiii-20-20202000000000000010−2i2i001-100-10ii−i−i000000
χ35222222-2-2-2-2-12-2-2-2-2-1-122-12-122-1-122111-2-2-2-1-1-1-1-1-11111111-2-11111-2-211-2-2−2i−2i2i2i-1-122-1-1-1-11111iiii−2i−2i−2i−2iiiiiiiii−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−i2020-20-20000000000000-10−2i2i00-110010ii−i−i000000
χ36222222-2-2-2-2-12-2-2-2-2-1-122-12-122-1-122111-2-2-2-1-1-1-1-1-11111111-2-11111-2-211-2-2−2i−2i2i2i-1-122-1-1-1-11111iiii−2i−2i−2i−2iiiiiiiii−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−i-20-202020000000000000102i−2i001-100-10−i−iii000000
χ372222-2-22-22-22222-2-222222222-2-2-2-2-22-2-22-2-222-2-2-2-222-2-2-2-22222222-2-2-2-22200002-22-222-2-222-2-200000000000000000000000000000000020-20-20200000000000002000000-220-20000000000
χ382222-2-22-22-22222-2-222222222-2-2-2-2-22-2-22-2-222-2-2-2-222-2-2-2-22222222-2-2-2-22200002-22-222-2-222-2-2000000000000000000000000000000000-202020-20000000000000-20000002-2020000000000
χ392222-2-22-22-222-2-2222222222-22-2-2-2-22-2-22-2-222-2-2-2-222-2-2-2-222222-2-22222-2-20000-22-22-2-222-2-2220000000000000000000000000000000020-20-2020000000000000200000-2200-200000000000
χ402222-2-22-22-222-2-2222222222-22-2-2-2-22-2-22-2-222-2-2-2-222-2-2-2-222222-2-22222-2-20000-22-22-2-222-2-22200000000000000000000000000000000-202020-20000000000000-2000002-200200000000000
χ412222-2-22-22-22-122-2-222-1-12-1-12-2-2-2112-2-2-111-1-11111-1-111112-1-1-1-12211-2-2-1-100002-2-11-1-111-1-1110000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i30000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i3020-20-2020000000000000-10000001-1010000−i3i3−i3i300
χ422222-2-22-22-22-122-2-222-1-12-1-12-2-2-2112-2-2-111-1-11111-1-111112-1-1-1-12211-2-2-1-100002-2-11-1-111-1-1110000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i30000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i30-202020-200000000000001000000-110-10000i3−i3i3−i300
χ432222-2-22-22-22-122-2-222-1-12-1-12-2-2-2112-2-2-111-1-11111-1-111112-1-1-1-12211-2-2-1-100002-2-11-1-111-1-1110000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i30000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3020-20-2020000000000000-10000001-1010000i3−i3i3−i300
χ442222-2-22-22-22-122-2-222-1-12-1-12-2-2-2112-2-2-111-1-11111-1-111112-1-1-1-12211-2-2-1-100002-2-11-1-111-1-1110000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i30000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i30-202020-200000000000001000000-110-10000−i3i3−i3i300
χ452222-2-22-22-2-12-2-222-1-122-12-1-2211-2-2-1112-2-2-1-11111-1-11111-12-1-1-11122-1-1-2-200001-1-2211-1-111-1-1−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i320-20-2020000000000000-1000001-10010−i3i3−i3i3000000
χ462222-2-22-22-2-12-2-222-1-122-12-1-2211-2-2-1112-2-2-1-11111-1-11111-12-1-1-11122-1-1-2-200001-1-2211-1-111-1-1−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3-202020-20000000000000100000-1100-10i3−i3i3−i3000000
χ472222-2-22-22-2-12-2-222-1-122-12-1-2211-2-2-1112-2-2-1-11111-1-11111-12-1-1-11122-1-1-2-200001-1-2211-1-111-1-1i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i320-20-2020000000000000-1000001-10010i3−i3i3−i3000000
χ482222-2-22-22-2-12-2-222-1-122-12-1-2211-2-2-1112-2-2-1-11111-1-11111-12-1-1-11122-1-1-2-200001-1-2211-1-111-1-1i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3-202020-20000000000000100000-1100-10−i3i3−i3i3000000
χ492222-2-2-22-222222-2-22222222-22-2-2-2-2-222-22222-2-2-2-2-2-22222-2-22-2-222-2-2-2-2220000-22-22-2-22222-2-20000000000000000000000000000000020-2020-20000000000000200000-2-200200000000000
χ502222-2-2-22-222222-2-22222222-22-2-2-2-2-222-22222-2-2-2-2-2-22222-2-22-2-222-2-2-2-2220000-22-22-2-22222-2-200000000000000000000000000000000-2020-2020000000000000-2000002200-200000000000
χ512222-2-2-22-2222-2-22222222222-2-2-2-2-2-222-22222-2-2-2-2-2-22222-2-22-2-2-2-22222-2-200002-22-222-2-2-2-22200000000000000000000000000000000020-2020-200000000000002000000-2-2020000000000
χ522222-2-2-22-2222-2-22222222222-2-2-2-2-2-222-22222-2-2-2-2-2-22222-2-22-2-2-2-22222-2-200002-22-222-2-2-2-222000000000000000000000000000000000-2020-2020000000000000-2000000220-20000000000
χ532222-2-2-22-222-1-2-22222-1-12-1-12-2-2-211-2221-1-1-1-1111111-1-1-1-1-21-111-2-2-1-1221100002-2-11-1-11111-1-1000033−3−33333−3−3−3−30000−3−333−3−3−3−33333020-2020-20000000000000-1000000110-100003−3−3300
χ542222-2-2-22-222-1-2-22222-1-12-1-12-2-2-211-2221-1-1-1-1111111-1-1-1-1-21-111-2-2-1-1221100002-2-11-1-11111-1-1000033−3−33333−3−3−3−30000−3−333−3−3−3−333330-2020-20200000000000001000000-1-1010000−333−300
χ552222-2-2-22-222-1-2-22222-1-12-1-12-2-2-211-2221-1-1-1-1111111-1-1-1-1-21-111-2-2-1-1221100002-2-11-1-11111-1-10000−3−333−3−3−3−33333000033−3−33333−3−3−3−3020-2020-20000000000000-1000000110-10000−333−300
χ562222-2-2-22-222-1-2-22222-1-12-1-12-2-2-211-2221-1-1-1-1111111-1-1-1-1-21-111-2-2-1-1221100002-2-11-1-11111-1-10000−3−333−3−3−3−33333000033−3−33333−3−3−3−30-2020-20200000000000001000000-1-10100003−3−3300
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.