Finite Group Databasebeta

← Group #72252326

Character table — Group #72252326

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size11112222222222222244444444444444444444444444444444444444448888888888888888888888888888888888888888888888882424242424242424363636364848484848484848484848484848484848484848727272727272
order122222222233666666344446666666666666666666666666661212121212121212444412121212121212121212121212121212121212121212121212121212121212121212121212121212121212122244444422226688881212121212122424242424242424224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-111-1-11-1-1-1-1-11-111-1-111-1-11-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-11-1-111-11-1-1-1-1-11-1-111-1-111-11-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1-11-1-1-11111-1-11-1-1-1-1-11111-1-11111
χ71111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-1-1111-1-1-1-111-111111-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111111111-1-1-1-1
χ9111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1ii−i−i11-1-11111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-1-1-111111111i−ii−i-1-1-1-111ii−i−iii−i−i-1-1ii−i−i
χ10111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1ii−i−i11-1-11111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1-1-1-1111-1-1-1-1-11-1i−i−ii-1-1111-1ii−i−i−i−iii11−i−iii
χ11111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1ii−i−i11-1-11111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1111-1-1-11-1-1-1-1-11−iii−i11-1-1-11−i−iiiii−i−i11−i−iii
χ12111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1ii−i−i11-1-11111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-11111-1-11111-1-1−ii−ii1111-1-1−i−iii−i−iii-1-1ii−i−i
χ13111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1−i−iii11-1-11111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii11-1-1-1-111111111−ii−ii-1-1-1-111−i−iii−i−iii-1-1−i−iii
χ14111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1−i−iii11-1-11111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1-1-1-1111-1-1-1-1-11-1−iii−i-1-1111-1−i−iiiii−i−i11ii−i−i
χ15111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1−i−iii11-1-11111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1111-1-1-11-1-1-1-1-11i−i−ii11-1-1-11ii−i−i−i−iii11ii−i−i
χ16111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1−i−iii11-1-11111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-11111-1-11111-1-1i−ii−i1111-1-1ii−i−iii−i−i-1-1−i−iii
χ172222222222222222222-2-2-2-2222222222222222222222222222-2-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-2000000000000000000002-20000
χ182222222222222222222-2-2-2-2222222222222222222222222222-2-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-22200000000000000000000-220000
χ1922222222222-122-1-12-1-1222222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-122222-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10200220200000-1002200-1-10-10000-1-1-1-1000000
χ2022222222222-122-1-12-1-1222222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-122222-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10-200-2-20-200000100-2-200110100001111000000
χ2122222222222-122-1-12-1-1222222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-1-2-2-2-22-12-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-21111111111110200220200000-100-2-200-1-10-100001111000000
χ2222222222222-122-1-12-1-1222222-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-122-1-1-2-2-2-22-12-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-21111111111110-200-2-20-200000100220011010000-1-1-1-1000000
χ232222222222-12-1-122-12-12222-1-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1222222-12-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1202200200000-102200-1-100-10-1-1-1-10000000000
χ242222222222-12-1-122-12-12222-1-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1222222-12-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-20-2-200-20000010-2-20011001011110000000000
χ252222222222-12-1-122-12-12222-1-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-122-2-2-2-2-12-12-1-1-1-1-1-1-1-11111-2-2-2-2111111111111-2-2-2-211111111202200200000-10-2-200-1-100-1011110000000000
χ262222222222-12-1-122-12-12222-1-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-122-2-2-2-2-12-12-1-1-1-1-1-1-1-11111-2-2-2-2111111111111-2-2-2-211111111-20-2-200-200000102200110010-1-1-1-10000000000
χ27222222-2-2-2-2222222222-2-2222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22-2-2-2-2-2-222220000-2-222-2-2-2-22222000000000000000000000000000000000000000022-2-200000000000000000000-220000
χ28222222-2-2-2-2222222222-2-2222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22-2-2-2-2-2-222220000-2-222-2-2-2-222220000000000000000000000000000000000000000-2-222000000000000000000002-20000
χ29222222-2-2-2-22-122-1-12-1-122-2-222-1-1-2-2-2111-1-1-1-1-1-1111111-21-11122-1-1-2-2112i2i−2i−2i2-1-21-1-1-1-111112i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiiiiiii0200-2-20200000-1002i−2i00110-10000−i−iii000000
χ30222222-2-2-2-22-122-1-12-1-122-2-222-1-1-2-2-2111-1-1-1-1-1-1111111-21-11122-1-1-2-2112i2i−2i−2i2-1-21-1-1-1-111112i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiiiiiii0-200220-200000100−2i2i00-1-1010000ii−i−i000000
χ31222222-2-2-2-22-122-1-12-1-122-2-222-1-1-2-2-2111-1-1-1-1-1-1111111-21-11122-1-1-2-211−2i−2i2i2i2-1-21-1-1-1-11111−2i−2i−2i−2iiiiiiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i0200-2-20200000-100−2i2i00110-10000ii−i−i000000
χ32222222-2-2-2-22-122-1-12-1-122-2-222-1-1-2-2-2111-1-1-1-1-1-1111111-21-11122-1-1-2-211−2i−2i2i2i2-1-21-1-1-1-11111−2i−2i−2i−2iiiiiiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i0-200220-2000001002i−2i00-1-1010000−i−iii000000
χ33222222-2-2-2-2-12-1-122-12-122-2-2-1-122111-2-2-2-1-1-1-1-1-11111111-2-111-1-12211-2-22i2i−2i−2i-121-2-1-1-1-11111−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−iiiii−2i−2i−2i−2iiiiiiiii20-2-200200000-102i−2i001100-10−i−iii0000000000
χ34222222-2-2-2-2-12-1-122-12-122-2-2-1-122111-2-2-2-1-1-1-1-1-11111111-2-111-1-12211-2-22i2i−2i−2i-121-2-1-1-1-11111−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−iiiii−2i−2i−2i−2iiiiiiiii-202200-20000010−2i2i00-1-10010ii−i−i0000000000
χ35222222-2-2-2-2-12-1-122-12-122-2-2-1-122111-2-2-2-1-1-1-1-1-11111111-2-111-1-12211-2-2−2i−2i2i2i-121-2-1-1-1-11111iiii−2i−2i−2i−2iiiiiiiii−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−i20-2-200200000-10−2i2i001100-10ii−i−i0000000000
χ36222222-2-2-2-2-12-1-122-12-122-2-2-1-122111-2-2-2-1-1-1-1-1-11111111-2-111-1-12211-2-2−2i−2i2i2i-121-2-1-1-1-11111iiii−2i−2i−2i−2iiiiiiiii−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−i-202200-200000102i−2i00-1-10010−i−iii0000000000
χ372222-2-22-22-22222222222-22-2-2-2-2-22-2-22-2-222-2-2-2-222-2-2-2-22222222-2-2-2-2220000-222-222-2-222-2-20000000000000000000000000000000002002-20-20000020000002-20-200000000000000
χ382222-2-22-22-22222222222-22-2-2-2-2-22-2-22-2-222-2-2-2-222-2-2-2-22222222-2-2-2-2220000-222-222-2-222-2-2000000000000000000000000000000000-200-220200000-2000000-220200000000000000
χ392222-2-22-22-2222222222-22-22-2-2-2-22-2-22-2-222-2-2-2-222-2-2-2-222222-2-22222-2-200002-2-22-2-222-2-22200000000000000000000000000000000202-200-2000002000002-200-2000000000000000
χ402222-2-22-22-2222222222-22-22-2-2-2-22-2-22-2-222-2-2-2-222-2-2-2-222222-2-22222-2-200002-2-22-2-222-2-22200000000000000000000000000000000-20-2200200000-200000-22002000000000000000
χ412222-2-22-22-22-122-1-12-1-12-22-2-2-2112-2-2-111-1-11111-1-111112-1-1-1-12211-2-2-1-10000-2-121-1-111-1-1110000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i30000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i302002-20-200000-1000000-11010000−i3i3−i3i3000000
χ422222-2-22-22-22-122-1-12-1-12-22-2-2-2112-2-2-111-1-11111-1-111112-1-1-1-12211-2-2-1-10000-2-121-1-111-1-1110000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i30000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i30-200-22020000010000001-10-10000i3−i3i3−i3000000
χ432222-2-22-22-22-122-1-12-1-12-22-2-2-2112-2-2-111-1-11111-1-111112-1-1-1-12211-2-2-1-10000-2-121-1-111-1-1110000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i30000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i302002-20-200000-1000000-11010000i3−i3i3−i3000000
χ442222-2-22-22-22-122-1-12-1-12-22-2-2-2112-2-2-111-1-11111-1-111112-1-1-1-12211-2-2-1-10000-2-121-1-111-1-1110000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i30000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i30-200-22020000010000001-10-10000−i3i3−i3i3000000
χ452222-2-22-22-2-12-1-122-12-1-22-2211-2-2-1112-2-2-1-11111-1-11111-12-1-1-11122-1-1-2-20000-1-21211-1-111-1-1−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3202-200-200000-100000-110010−i3i3−i3i30000000000
χ462222-2-22-22-2-12-1-122-12-1-22-2211-2-2-1112-2-2-1-11111-1-11111-12-1-1-11122-1-1-2-20000-1-21211-1-111-1-1−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3-20-22002000001000001-100-10i3−i3i3−i30000000000
χ472222-2-22-22-2-12-1-122-12-1-22-2211-2-2-1112-2-2-1-11111-1-11111-12-1-1-11122-1-1-2-20000-1-21211-1-111-1-1i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3202-200-200000-100000-110010i3−i3i3−i30000000000
χ482222-2-22-22-2-12-1-122-12-1-22-2211-2-2-1112-2-2-1-11111-1-11111-12-1-1-11122-1-1-2-20000-1-21211-1-111-1-1i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3-20-22002000001000001-100-10−i3i3−i3i30000000000
χ492222-2-2-22-222222222222-2-22-2-2-2-2-222-22222-2-2-2-2-2-22222-2-22-2-222-2-222-2-20000-22-2222-2-2-2-222000000000000000000000000000000000200-220-2000002000000-220-200000000000000
χ502222-2-2-22-222222222222-2-22-2-2-2-2-222-22222-2-2-2-2-2-22222-2-22-2-222-2-222-2-20000-22-2222-2-2-2-222000000000000000000000000000000000-2002-20200000-20000002-20200000000000000
χ512222-2-2-22-22222222222-222-2-2-2-2-2-222-22222-2-2-2-2-2-22222-2-22-2-2-2-222-2-22200002-22-2-2-22222-2-20000000000000000000000000000000020-2200-200000200000-2200-2000000000000000
χ522222-2-2-22-22222222222-222-2-2-2-2-2-222-22222-2-2-2-2-2-22222-2-22-2-2-2-222-2-22200002-22-2-2-22222-2-200000000000000000000000000000000-202-200200000-2000002-2002000000000000000
χ532222-2-2-22-222-122-1-12-1-12-2-22-2-211-2221-1-1-1-1111111-1-1-1-1-21-111221122110000-2-1-2-1-1-11111-1-1000033−3−33333−3−3−3−30000−3−333−3−3−3−333330200-220-200000-10000001-10100003−3−33000000
χ542222-2-2-22-222-122-1-12-1-12-2-22-2-211-2221-1-1-1-1111111-1-1-1-1-21-111221122110000-2-1-2-1-1-11111-1-1000033−3−33333−3−3−3−30000−3−333−3−3−3−333330-2002-202000001000000-110-10000−333−3000000
χ552222-2-2-22-222-122-1-12-1-12-2-22-2-211-2221-1-1-1-1111111-1-1-1-1-21-111221122110000-2-1-2-1-1-11111-1-10000−3−333−3−3−3−33333000033−3−33333−3−3−3−30200-220-200000-10000001-1010000−333−3000000
χ562222-2-2-22-222-122-1-12-1-12-2-22-2-211-2221-1-1-1-1111111-1-1-1-1-21-111221122110000-2-1-2-1-1-11111-1-10000−3−333−3−3−3−33333000033−3−33333−3−3−3−30-2002-202000001000000-110-100003−3−33000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.