Finite Group Databasebeta

← Group #11923336

Character table — Group #11923336

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222334444444446666688888888888812121212121212121212121616161616161616161618182424242424242424243232323236363648484848
order123468844233466122424224883366612121224242424224468121212121266121212122424242424666122424242424661212248661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111−1−i32−1+i321−1−i32−1+i3211111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32
χ31111111111−1+i32−1−i321−1+i32−1−i3211111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32
χ4111111111-111-1111111111111-111-1111111-1-1-1-11111111-1-1-1-111111111-111-111111-1-1-1-1-1-11-1-1-1-1
χ5111111111-1−1−i32−1+i32-1−1−i32−1+i3211111111−1−i32−1+i32-1−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1111−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1−1−i32−1+i32-11−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32-1-111+i321−i321+i321−i32
χ6111111111-1−1+i32−1−i32-1−1+i32−1−i3211111111−1+i32−1−i32-1−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1111−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1−1+i32−1−i32-11−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32-1-111−i321+i321−i321+i32
χ71111111-1-11111111111-11-1-11111111111111-11-1111-1-1-1-11111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1
χ81111111-1-11−1−i32−1+i321−1−i32−1+i321111-11-1-1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-11-11111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111+i321−i32111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321−i32
χ91111111-1-11−1+i32−1−i321−1+i32−1−i321111-11-1-1−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-11-11111−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−i321+i32111−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321+i32
χ101111111-1-1-111-1111111-11-1-111-111-1111111-11-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-11111
χ111111111-1-1-1−1−i32−1+i32-1−1−i32−1+i321111-11-1-1−1−i32−1+i32-1−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-111111+i321+i321−i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321−i32-111+i321+i321−i321−i321+i321−i321+i321−i3211-1−1−i32−1+i32−1−i32−1+i32
χ121111111-1-1-1−1+i32−1−i32-1−1+i32−1−i321111-11-1-1−1+i32−1−i32-1−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-111111−i321−i321+i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321+i32-111−i321−i321+i321+i321−i321+i321−i321+i3211-1−1+i32−1−i32−1+i32−1−i32
χ1311111-1-111111-1111-1-1111-1-111111-111-1-1-1-1-1-1111-11111111-1-111-1-1-1-111-1111-1-1-1-1-111-1-11-1-1-1-111
χ1411111-1-1111−1−i32−1+i32-1−1−i32−1+i321-1-1111-1-1−1−i32−1+i321−1−i32−1+i32-1−1−i32−1+i321+i321+i321−i321−i32-1-1111-11−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i3211-1−1−i32−1+i321-11+i321+i321−i321−i32−1−i32−1+i321+i321−i321-1-11+i321−i32−1−i32−1+i32
χ1511111-1-1111−1+i32−1−i32-1−1+i32−1−i321-1-1111-1-1−1+i32−1−i321−1+i32−1−i32-1−1+i32−1−i321−i321−i321+i321+i32-1-1111-11−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i3211-1−1+i32−1−i321-11−i321−i321+i321+i32−1+i32−1−i321−i321+i321-1-11−i321+i32−1+i32−1−i32
χ1611111-1-111-1111111-1-1111-1-111-111111-1-1-1-111-1-11-111111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111-11-111-1-1
χ1711111-1-111-1−1−i32−1+i321−1−i32−1+i321-1-1111-1-1−1−i32−1+i32-1−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i3211-1-11-11−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32111−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i32−1−i32−1+i32-11-1−1−i32−1+i321+i321−i32
χ1811111-1-111-1−1+i32−1−i321−1+i32−1−i321-1-1111-1-1−1+i32−1−i32-1−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i3211-1-11-11−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32111−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i32−1+i32−1−i32-11-1−1+i32−1−i321−i321+i32
χ1911111-1-1-1-1111-1111-1-11-111111111-111-1-1-1-1-111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1111111-1-1-11111-1-1
χ2011111-1-1-1-11−1−i32−1+i32-1−1−i32−1+i321-1-11-1111−1−i32−1+i321−1−i32−1+i32-1−1−i32−1+i321+i321+i321−i321−i32-111-11-111+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32-1-1-11+i321−i321-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i32-111−1−i32−1+i321+i321−i32
χ2111111-1-1-1-11−1+i32−1−i32-1−1+i32−1−i321-1-11-1111−1+i32−1−i321−1+i32−1−i32-1−1+i32−1−i321−i321−i321+i321+i32-111-11-111−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32-1-1-11−i321+i321-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i32-111−1+i32−1−i321−i321+i32
χ2211111-1-1-1-1-1111111-1-11-111111-111111-1-1-1-11-1-111-11-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-1-11111-1-1111-11-1-111
χ2311111-1-1-1-1-1−1−i32−1+i321−1−i32−1+i321-1-11-1111−1−i32−1+i32-1−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i321-1-111-111+i321+i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-111+i321−i32-1-1−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i321-111+i321−i32−1−i32−1+i32
χ2411111-1-1-1-1-1−1+i32−1−i321−1+i32−1−i321-1-11-1111−1+i32−1−i32-1−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i321-1-111-111−i321−i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-111−i321+i32-1-1−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1−i321-111−i321+i32−1+i32−1−i32
χ25222-220022022022-200-2-2200220220-2-200000000-20222220000-2-200002-20-2-200000000000000000
χ26222-2200220−1−i3−1+i30−1−i3−1+i3-200-2-2200−1−i3−1+i30−1−i3−1+i301+i31−i300000000-202−1−i3−1−i3−1+i3−1+i300001+i31−i300002-201+i31−i300000000000000000
χ27222-2200220−1+i3−1−i30−1+i3−1−i3-200-2-2200−1+i3−1−i30−1+i3−1−i301−i31+i300000000-202−1+i3−1+i3−1−i3−1−i300001−i31+i300002-201−i31+i300000000000000000
χ28222-2200-2-2022022-200-22200220220-2-200000000-202-2-2-2-20000-2-20000-2202200000000000000000
χ29222-2200-2-20−1−i3−1+i30−1−i3−1+i3-200-22200−1−i3−1+i30−1−i3−1+i301+i31−i300000000-2021+i31+i31−i31−i300001+i31−i30000-220−1−i3−1+i300000000000000000
χ30222-2200-2-20−1+i3−1−i30−1+i3−1−i3-200-22200−1+i3−1−i30−1+i3−1−i301−i31+i300000000-2021−i31−i31+i31+i300001−i31+i30000-220−1+i3−1−i300000000000000000
χ3122-12-12200222222-1-1-120200-1-1-1-1-1-12222222020-12-100002222-1-1-1-1-1-100-100-1-10000-1-1-1-10000000
χ3222-12-122002−1−i3−1+i32−1−i3−1+i3-1-1-1202001+i321−i32-11+i321−i32-1−1−i3−1+i3−1−i3−1−i3−1+i3−1+i32020-12-10000−1−i3−1+i3−1−i3−1+i31+i321−i321+i321+i321−i321−i3200-100-1-100001+i321−i321+i321−i320000000
χ3322-12-122002−1+i3−1−i32−1+i3−1−i3-1-1-1202001−i321+i32-11−i321+i32-1−1+i3−1−i3−1+i3−1+i3−1−i3−1−i32020-12-10000−1+i3−1−i3−1+i3−1−i31−i321+i321−i321−i321+i321+i3200-100-1-100001−i321+i321−i321+i320000000
χ3422-12-12200-222-222-1-1-120200-1-11-1-11222222-20-20-12-10000-2-2-2-2-1-1-1-1-1-1001001-1000011110000000
χ3522-12-12200-2−1−i3−1+i3-2−1−i3−1+i3-1-1-1202001+i321−i3211+i321−i321−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-20-20-12-100001+i31−i31+i31−i31+i321−i321+i321+i321−i321−i32001001-10000−1−i32−1+i32−1−i32−1+i320000000
χ3622-12-12200-2−1+i3−1−i3-2−1+i3−1−i3-1-1-1202001−i321+i3211−i321+i321−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-20-20-12-100001−i31+i31−i31+i31−i321+i321−i321−i321+i321+i32001001-10000−1+i32−1−i32−1+i32−1−i320000000
χ3722-12-1-2-200222-222-11120200-1-1-1-1-1122-2-2-2-2-2020-1-2-1000022-2-2-1-1111100100-110000-1-1110000000
χ3822-12-1-2-2002−1−i3−1+i3-2−1−i3−1+i3-111202001+i321−i32-11+i321−i321−1−i3−1+i31+i31+i31−i31−i3-2020-1-2-10000−1−i3−1+i31+i31−i31+i321−i32−1−i32−1−i32−1+i32−1+i3200100-1100001+i321−i32−1−i32−1+i320000000
χ3922-12-1-2-2002−1+i3−1−i3-2−1+i3−1−i3-111202001−i321+i32-11−i321+i321−1+i3−1−i31−i31−i31+i31+i3-2020-1-2-10000−1+i3−1−i31−i31+i31−i321+i32−1+i32−1+i32−1−i32−1−i3200100-1100001−i321+i32−1+i32−1−i320000000
χ4022-12-1-2-200-222222-11120200-1-11-1-1-122-2-2-2-220-20-1-2-10000-2-222-1-1111100-10011000011-1-10000000
χ4122-12-1-2-200-2−1−i3−1+i32−1−i3−1+i3-111202001+i321−i3211+i321−i32-1−1−i3−1+i31+i31+i31−i31−i320-20-1-2-100001+i31−i3−1−i3−1+i31+i321−i32−1−i32−1−i32−1+i32−1+i3200-100110000−1−i32−1+i321+i321−i320000000
χ4222-12-1-2-200-2−1+i3−1−i32−1+i3−1−i3-111202001−i321+i3211−i321+i32-1−1+i3−1−i31−i31−i31+i31+i320-20-1-2-100001−i31+i3−1+i3−1−i31−i321+i32−1+i32−1+i32−1−i32−1−i3200-100110000−1+i32−1−i321−i321+i320000000
χ43333333333300300333-13-133003003000000-13-13-1-1-100000000000000-1-1-100-1-100000000-1-1-10000
χ44333333333-300-300333-13-13300-300-30000001-31-3-1-1-100000000000000-1-11001-10000000011-10000
χ453333333-3-3300300333-1-3-1-3-3003003000000-1-3-1-3-1-1-10000000000000011-100-1-1000000001110000
χ463333333-3-3-300-300333-1-3-1-3-300-300-30000001313-1-1-100000000000000111001-100000000-1-110000
χ4733333-3-333300-3003-3-3-13-1-3-300300-30000001-3-13-11-100000000000000-1-1100-1100000000-1110000
χ4833333-3-333-3003003-3-3-13-1-3-300-3003000000-131-3-11-100000000000000-1-1-10011000000001-110000
χ4933333-3-3-3-3300-3003-3-3-1-3-13300300-300000013-1-3-11-10000000000000011100-11000000001-1-10000
χ5033333-3-3-3-3-3003003-3-3-1-3-13300-3003000000-1-313-11-10000000000000011-1001100000000-11-10000
χ5144-2-4-20000044044200-40400-2-20-2-20-4-40000000020-2000000002200000000000000000000000000
χ5244-2-4-200000−2−2i3−2+2i30−2−2i3−2+2i3200-404001+i31−i301+i31−i302+2i32−2i30000000020-200000000−1−i3−1+i300000000000000000000000000
χ5344-2-4-200000−2+2i3−2−2i30−2+2i3−2−2i3200-404001−i31+i301−i31+i302−2i32+2i30000000020-200000000−1+i3−1−i300000000000000000000000000
χ544-440-4−2i22i24i−4i0-2-20220−2i22i200022−22-2-2022000−i2i2−i2i200000002i−2i2i−2i000000−i2i2−i2i200000002−22−200000000000
χ554-440-4−2i22i24i−4i01+i31−i30−1−i3−1+i30−2i22i200022−221+i31−i30−1−i3−1+i3000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ2300000002ζ22−2ζ222ζ14−2ζ14000000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ230000000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ2300000000000
χ564-440-4−2i22i24i−4i01−i31+i30−1+i3−1−i30−2i22i200022−221−i31+i30−1+i3−1−i3000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ1300000002ζ14−2ζ142ζ22−2ζ22000000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ130000000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ1300000000000
χ574-440-4−2i22i2−4i4i0-2-20220−2i22i2000−2222-2-2022000−i2i2−i2i20000000−2i2i−2i2i000000−i2i2−i2i20000000−22−2200000000000
χ584-440-4−2i22i2−4i4i01+i31−i30−1−i3−1+i30−2i22i2000−22221+i31−i30−1−i3−1+i3000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ230000000−2ζ222ζ22−2ζ142ζ14000000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ230000000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ2300000000000
χ594-440-4−2i22i2−4i4i01−i31+i30−1+i3−1−i30−2i22i2000−22221−i31+i30−1+i3−1−i3000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ130000000−2ζ142ζ14−2ζ222ζ22000000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ130000000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ1300000000000
χ604-440-42i2−2i24i−4i0-2-202202i2−2i2000−2222-2-2022000i2−i2i2−i200000002i−2i2i−2i000000i2−i2i2−i20000000−22−2200000000000
χ614-440-42i2−2i24i−4i01+i31−i30−1−i3−1+i302i2−2i2000−22221+i31−i30−1−i3−1+i3000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ2300000002ζ22−2ζ222ζ14−2ζ14000000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ230000000ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ2300000000000
χ624-440-42i2−2i24i−4i01−i31+i30−1+i3−1−i302i2−2i2000−22221−i31+i30−1+i3−1−i3000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ1300000002ζ14−2ζ142ζ22−2ζ22000000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ130000000−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ1300000000000
χ634-440-42i2−2i2−4i4i0-2-202202i2−2i200022−22-2-2022000i2−i2i2−i20000000−2i2i−2i2i000000i2−i2i2−i200000002−22−200000000000
χ644-440-42i2−2i2−4i4i01+i31−i30−1−i3−1+i302i2−2i200022−221+i31−i30−1−i3−1+i3000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ230000000−2ζ222ζ22−2ζ142ζ14000000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ230000000−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ2300000000000
χ654-440-42i2−2i2−4i4i01−i31+i30−1+i3−1−i302i2−2i200022−221−i31+i30−1+i3−1−i3000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ130000000−2ζ142ζ14−2ζ222ζ22000000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ130000000ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ1300000000000
χ66666-660066000000-6002-6-200000000000000000020-200000000000000-2200000000000000000000
χ67666-6600-6-6000000-60026-200000000000000000020-2000000000000002-200000000000000000000
χ6866-36-36600600600-3-3-3-20-20000-300-3000000-20-201-21000000000000000010011000000000000000
χ6966-36-36600-600-600-3-3-3-20-20000300300000020201-210000000000000000-100-11000000000000000
χ7066-36-3-6-600600-600-333-20-20000-300300000020-201210000000000000000-1001-1000000000000000
χ7166-36-3-6-600-600600-333-20-20000300-3000000-20201210000000000000000100-1-1000000000000000
χ728-8-404−4i24i2000-4-404402i2−2i200000220-2-2000−2i22i2−2i22i200000000000000000i2−i2i2−i20000000000000000000000
χ738-8-404−4i24i20002+2i32−2i30−2−2i3−2+2i302i2−2i200000−1−i3−1+i301+i31−i30002ζ7+2ζ13−2ζ7−2ζ132ζ5+2ζ23−2ζ5−2ζ2300000000000000000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ230000000000000000000000
χ748-8-404−4i24i20002−2i32+2i30−2+2i3−2−2i302i2−2i200000−1+i3−1−i301−i31+i30002ζ5+2ζ23−2ζ5−2ζ232ζ7+2ζ13−2ζ7−2ζ1300000000000000000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ130000000000000000000000
χ758-8-4044i2−4i2000-4-40440−2i22i200000220-2-20002i2−2i22i2−2i200000000000000000−i2i2−i2i20000000000000000000000
χ768-8-4044i2−4i20002+2i32−2i30−2−2i3−2+2i30−2i22i200000−1−i3−1+i301+i31−i3000−2ζ7−2ζ132ζ7+2ζ13−2ζ5−2ζ232ζ5+2ζ2300000000000000000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ230000000000000000000000
χ778-8-4044i2−4i20002−2i32+2i30−2+2i3−2−2i30−2i22i200000−1+i3−1−i301−i31+i3000−2ζ5−2ζ232ζ5+2ζ23−2ζ7−2ζ132ζ7+2ζ1300000000000000000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ130000000000000000000000
χ781212-6-12-6000000000060040-4000000000000000000-202000000000000000000000000000000000000

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