Finite Group Databasebeta

← Group #11797886

Character table — Group #11797886

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222222444444444444444488888888121212121212121212121212121212121212121212121212161616161616161618181818242424243636484848487272
order1244233466888812121212366612121212242424242424242424612242424241616161616161616484848484848484848484848484848486666121212128888248844612242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ51111111111111111111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ81111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ911-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−i1-1i−ii−i1-1i−ii−i
χ1011-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-11-1-1111-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii1-1−ii−ii1-1−ii−ii
χ1111-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-11-1-1111-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−iii-11i−i−ii-11i−i−ii
χ1211-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-11-1-1111-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1ii−i−i-11−iii−i-11−iii−i
χ1311-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-1-11-1111-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111ii−i−i-11−iii−i-11−ii−ii
χ1411-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-1-11-1111-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−iii-11i−i−ii-11i−ii−i
χ1511-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-1-11-1111-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-11111−i−iii1-1−ii−ii1-1−iii−i
χ1611-1-1-11111111-1-1-1-1-1-11-1-11-1-11111-1-111-1-1-11-1111-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-1-1-11111ii−i−i1-1i−ii−i1-1i−i−ii
χ172222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-20022-2-2-2-20000000000000000000000000000000022220000-2-2000000
χ182222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-20022-2-2-2-200000000000000000000000000000000-2-2-2-2000022000000
χ19222222-122-12222-1-122-12-1-1-1-12-122-1-1-1-12222-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000002-1-1-12-1-1-10000220000-1-10000
χ20222222-122-12222-1-122-12-1-1-1-12-122-1-1-1-12222-1-1-1-1-1-1-2-2-2-2000011111111000000002-1-1-12-1-1-10000-2-20000110000
χ21222222-122-12222-1-122-12-1-1-1-12-122-1-1-1-122-2-2-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000-2111-21110000-2-20000110000
χ22222222-122-12222-1-122-12-1-1-1-12-122-1-1-1-122-2-2-1-1-1-1-1-1-2-2-2-200001111111100000000-2111-21110000220000-1-10000
χ2322222-122-12222222-1-1-1-12-1-1-1-12-1-12222-1-122-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1-12-1-1-12-1-1000000220000-1-100
χ2422222-122-12222222-1-1-1-12-1-1-1-12-1-12222-1-122-1-1-1-1-1-10000-2-2-2-20000000011111111-12-1-1-12-1-1000000-2-200001100
χ2522222-122-12222222-1-1-1-12-1-1-1-12-1-12222-1-1-2-2-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-11-2111-211000000-2-200001100
χ2622222-122-12222222-1-1-1-12-1-1-1-12-1-12222-1-1-2-2-1-1-1-1-1-10000-2-2-2-200000000111111111-2111-211000000220000-1-100
χ272222-222-222000022222-2-2222-2-20000000000-2-200002−22−22−22−222−2−222−2−222−2−222−2−2000000002-22-2000000000000
χ282222-222-222000022222-2-2222-2-20000000000-2-200002−22−2−22−2222−2−222−2−2−2−222−2−22200000000-22-22000000000000
χ292222-222-222000022222-2-2222-2-20000000000-2-20000−22−222−22−2−2−222−2−22222−2−222−2−200000000-22-22000000000000
χ302222-222-222000022222-2-2222-2-20000000000-2-20000−22−22−22−22−2−222−2−222−2−222−2−222000000002-22-2000000000000
χ3122-2-2222-2220000-2-2-2-22222-2-2-2-200000000002-200002−2−22−i2i2i2−i222−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000−2i2i2i−2i000000000000
χ3222-2-2222-2220000-2-2-2-22222-2-2-2-200000000002-200002−2−22i2−i2−i2i222−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000002i−2i−2i2i000000000000
χ3322-2-2222-2220000-2-2-2-22222-2-2-2-200000000002-20000−222−2−i2i2i2−i2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000002i−2i−2i2i000000000000
χ3422-2-2222-2220000-2-2-2-22222-2-2-2-200000000002-20000−222−2i2−i2−i2i2−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000−2i2i2i−2i000000000000
χ3522-2-2-222222-2-222-2-2-2-22-2-22-2-222-2-222-2-22200-22-2-222000000000000000000000000000000002i2i−2i−2i0000−2i2i000000
χ3622-2-2-222222-2-222-2-2-2-22-2-22-2-222-2-222-2-22200-22-2-22200000000000000000000000000000000−2i−2i2i2i00002i−2i000000
χ3722-2-2-22-122-122-2-211-2-2-1-21-1112-12211-1-1-2-22-21-1-1-11122-2-20000-1-1-1-11111000000002-1-1-1-211100002-20000-110000
χ3822-2-2-22-122-122-2-211-2-2-1-21-1112-12211-1-1-2-22-21-1-1-111-2-22200001111-1-1-1-1000000002-1-1-1-21110000-2200001-10000
χ3922-2-2-22-122-122-2-211-2-2-1-21-1112-12211-1-1-2-2-221-1-1-11122-2-20000-1-1-1-1111100000000-21112-1-1-10000-2200001-10000
χ4022-2-2-22-122-122-2-211-2-2-1-21-1112-12211-1-1-2-2-221-1-1-111-2-22200001111-1-1-1-100000000-21112-1-1-100002-20000-110000
χ4122-2-2-2-122-1222-2-2-2-211-11-2-111-12-1-1-2-222112-21-1-1-11100002i2i−2i−2i00000000−i−i−i−iiiii-12-1-11-2110000002i−2i0000−ii00
χ4222-2-2-2-122-1222-2-2-2-211-11-2-111-12-1-1-2-222112-21-1-1-1110000−2i−2i2i2i00000000iiii−i−i−i−i-12-1-11-211000000−2i2i0000i−i00
χ4322-2-2-2-122-1222-2-2-2-211-11-2-111-12-1-1-2-22211-221-1-1-11100002i2i−2i−2i00000000−i−i−i−iiiii1-211-12-1-1000000−2i2i0000i−i00
χ4422-2-2-2-122-1222-2-2-2-211-11-2-111-12-1-1-2-22211-221-1-1-1110000−2i−2i2i2i00000000iiii−i−i−i−i1-211-12-1-10000002i−2i0000−ii00
χ45444444-244-2-4-4-4-4-2-244-24-2-2-2-24-2-4-42222-4-400-2-22222000000000000000000000000000000000000000000000000
χ4644444-244-24-4-4-4-444-2-2-2-24-2-2-2-2422-4-4-4-42200-2-22222000000000000000000000000000000000000000000000000
χ4744444-2-24-2-24444-2-2-2-21-2-2111-2-2-2-2-2-2-2-2-2-244111111000000000000000000000000-2-211-2-2110000000000000000
χ4844444-2-24-2-24444-2-2-2-21-2-2111-2-2-2-2-2-2-2-2-2-2-4-411111100000000000000000000000022-1-122-1-10000000000000000
χ4944444-2-24-2-2-4-4-4-4-2-2-2-21-2-2111-2-2222222220011-1-1-1-1000000000000000000000000003-3003-30000000000000000
χ5044444-2-24-2-2-4-4-4-4-2-2-2-21-2-2111-2-2222222220011-1-1-1-100000000000000000000000000-3300-330000000000000000
χ514444-44-2-44-20000-2-244-2-42-2-2-2-42000000000022000022−2222−220000−2−222−2−22200000000000000000000000000000000
χ524444-44-2-44-20000-2-244-2-42-2-2-2-420000000000220000−2222−2222000022−2−222−2−200000000000000000000000000000000
χ534444-4-24-4-24000044-2-2-22-4-2-2-22-40000000000220000000022−2222−2200000000−2−222−2−222000000000000000000000000
χ544444-4-24-4-24000044-2-2-22-4-2-2-22-400000000002200000000−2222−22220000000022−2−222−2−2000000000000000000000000
χ5544-4-444-2-44-2000022-4-4-24-2-222-420000000000-22000022−22−22220000−2−22222−2−200000000000000000000000000000000
χ5644-4-444-2-44-2000022-4-4-24-2-222-420000000000-220000−222222−22000022−2−2−2−22200000000000000000000000000000000
χ5744-4-44-24-4-240000-4-422-2-24-2222-40000000000-2200000000−2i22i22i2−2i200000000i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ5844-4-44-24-4-240000-4-422-2-24-2222-40000000000-22000000002i2−2i2−2i22i200000000−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ5944-4-4-44-244-2-4-44422-4-4-2-42-2224-2-4-4-2-22244002-222-2-2000000000000000000000000000000000000000000000000
χ6044-4-4-4-244-24-4-444-4-422-22-4-222-242244-4-4-2-2002-222-2-2000000000000000000000000000000000000000000000000
χ6144-4-4-4-2-24-2-244-4-422221221-1-1-2-2-2-222-2-2224-4-1111-1-1000000000000000000000000-2-21122-1-10000000000000000
χ6244-4-4-4-2-24-2-244-4-422221221-1-1-2-2-2-222-2-222-44-1111-1-100000000000000000000000022-1-1-2-2110000000000000000
χ6344-4-4-4-2-24-2-2-4-44422221221-1-1-2-222-2-222-2-200-11-1-111000000000000000000000000003-300-330000000000000000
χ6444-4-4-4-2-24-2-2-4-44422221221-1-1-2-222-2-222-2-200-11-1-11100000000000000000000000000-33003-30000000000000000
χ654-44i−4i0440-4-422−22−2i22i24i−4i4i−4i400-44i−4i0022−22−2i22i222−22−2i22i2000022−22−2i22i2000000000000000000000000000000000000000000000000
χ664-44i−4i0440-4-4−22222i2−2i24i−4i4i−4i400-44i−4i00−22222i2−2i2−22222i2−2i20000−22222i2−2i2000000000000000000000000000000000000000000000000
χ674-44i−4i04-20-4222−22−2i22i2−2i2i4i−4i-2002−2i2i0022−22i2−i2−22−2i22i20000−22i2−i200000000−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ4300000000000000000000000000000000
χ684-44i−4i04-20-4222−22−2i22i2−2i2i4i−4i-2002−2i2i0022−22i2−i2−22−2i22i20000−22i2−i200000000ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ4300000000000000000000000000000000
χ694-44i−4i04-20-42−22222i2−2i2−2i2i4i−4i-2002−2i2i00−2222−i2i22−22i2−2i200002−2−i2i200000000−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ4700000000000000000000000000000000
χ704-44i−4i04-20-42−22222i2−2i2−2i2i4i−4i-2002−2i2i00−2222−i2i22−22i2−2i200002−2−i2i200000000ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ4700000000000000000000000000000000
χ714-44i−4i0-2402-422−22−2i22i24i−4i−2i2i-2002−2i2i00−22−2i22i222−22i2−i20000−22i2−i20000000000000000ζ13−ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47−ζ11−ζ25+ζ41+ζ43ζ11+ζ25−ζ41−ζ43ζ11−ζ25+ζ41−ζ43−ζ11+ζ25−ζ41+ζ43ζ13−ζ29−ζ31+ζ47−ζ13+ζ29+ζ31−ζ47000000000000000000000000
χ724-44i−4i0-2402-422−22−2i22i24i−4i−2i2i-2002−2i2i00−22−2i22i222−22i2−i20000−22i2−i20000000000000000−ζ13+ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47ζ11+ζ25−ζ41−ζ43−ζ11−ζ25+ζ41+ζ43−ζ11+ζ25−ζ41+ζ43ζ11−ζ25+ζ41−ζ43−ζ13+ζ29+ζ31−ζ47ζ13−ζ29−ζ31+ζ47000000000000000000000000
χ734-44i−4i0-2402-4−22222i2−2i24i−4i−2i2i-2002−2i2i002−22i2−2i2−2222−i2i200002−2−i2i20000000000000000−ζ11−ζ25+ζ41+ζ43ζ11+ζ25−ζ41−ζ43−ζ13+ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47−ζ13+ζ29+ζ31−ζ47ζ13−ζ29−ζ31+ζ47ζ11−ζ25+ζ41−ζ43−ζ11+ζ25−ζ41+ζ43000000000000000000000000
χ744-44i−4i0-2402-4−22222i2−2i24i−4i−2i2i-2002−2i2i002−22i2−2i2−2222−i2i200002−2−i2i20000000000000000ζ11+ζ25−ζ41−ζ43−ζ11−ζ25+ζ41+ζ43ζ13−ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47ζ13−ζ29−ζ31+ζ47−ζ13+ζ29+ζ31−ζ47−ζ11+ζ25−ζ41+ζ43ζ11−ζ25+ζ41−ζ43000000000000000000000000
χ754-4−4i4i0440-4-422−222i2−2i2−4i4i−4i4i400-4−4i4i0022−222i2−2i222−222i2−2i2000022−222i2−2i2000000000000000000000000000000000000000000000000
χ764-4−4i4i0440-4-4−2222−2i22i2−4i4i−4i4i400-4−4i4i00−2222−2i22i2−2222−2i22i20000−2222−2i22i2000000000000000000000000000000000000000000000000
χ774-4−4i4i04-20-4222−222i2−2i22i−2i−4i4i-20022i−2i0022−22−i2i2−222i2−2i20000−22−i2i200000000−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ4300000000000000000000000000000000
χ784-4−4i4i04-20-4222−222i2−2i22i−2i−4i4i-20022i−2i0022−22−i2i2−222i2−2i20000−22−i2i200000000ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ4300000000000000000000000000000000
χ794-4−4i4i04-20-42−2222−2i22i22i−2i−4i4i-20022i−2i00−2222i2−i22−2−2i22i200002−2i2−i200000000−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ4700000000000000000000000000000000
χ804-4−4i4i04-20-42−2222−2i22i22i−2i−4i4i-20022i−2i00−2222i2−i22−2−2i22i200002−2i2−i200000000ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ4700000000000000000000000000000000
χ814-4−4i4i0-2402-422−222i2−2i2−4i4i2i−2i-20022i−2i00−222i2−2i222−22−i2i20000−22−i2i20000000000000000ζ11−ζ25+ζ41−ζ43−ζ11+ζ25−ζ41+ζ43−ζ13+ζ29+ζ31−ζ47ζ13−ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47ζ11+ζ25−ζ41−ζ43−ζ11−ζ25+ζ41+ζ43000000000000000000000000
χ824-4−4i4i0-2402-422−222i2−2i2−4i4i2i−2i-20022i−2i00−222i2−2i222−22−i2i20000−22−i2i20000000000000000−ζ11+ζ25−ζ41+ζ43ζ11−ζ25+ζ41−ζ43ζ13−ζ29−ζ31+ζ47−ζ13+ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47−ζ11−ζ25+ζ41+ζ43ζ11+ζ25−ζ41−ζ43000000000000000000000000
χ834-4−4i4i0-2402-4−2222−2i22i2−4i4i2i−2i-20022i−2i002−2−2i22i2−2222i2−i200002−2i2−i20000000000000000ζ13−ζ29−ζ31+ζ47−ζ13+ζ29+ζ31−ζ47ζ11−ζ25+ζ41−ζ43−ζ11+ζ25−ζ41+ζ43ζ11+ζ25−ζ41−ζ43−ζ11−ζ25+ζ41+ζ43−ζ13+ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47000000000000000000000000
χ844-4−4i4i0-2402-4−2222−2i22i2−4i4i2i−2i-20022i−2i002−2−2i22i2−2222i2−i200002−2i2−i20000000000000000−ζ13+ζ29+ζ31−ζ47ζ13−ζ29−ζ31+ζ47−ζ11+ζ25−ζ41+ζ43ζ11−ζ25+ζ41−ζ43−ζ11−ζ25+ζ41+ζ43ζ11+ζ25−ζ41−ζ43ζ13−ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47000000000000000000000000
χ858888-8-4-4-8-4-40000-4-4-4-4244222440000000000-2-20000000000000000000000000000000000000000000000000000
χ8688-8-88-4-4-8-4-4000044442-4-42-2-24400000000002-20000000000000000000000000000000000000000000000000000
χ878-88i−8i0-4-404442−42−4i24i2−4i4i−4i4i200-22i−2i00−22222i2−2i2−22222i2−2i200002−2−i2i2000000000000000000000000000000000000000000000000
χ888-88i−8i0-4-4044−42424i2−4i2−4i4i−4i4i200-22i−2i0022−22−2i22i222−22−2i22i20000−22i2−i2000000000000000000000000000000000000000000000000
χ898-8−8i8i0-4-404442−424i2−4i24i−4i4i−4i200-2−2i2i00−2222−2i22i2−2222−2i22i200002−2i2−i2000000000000000000000000000000000000000000000000
χ908-8−8i8i0-4-4044−4242−4i24i24i−4i4i−4i200-2−2i2i0022−222i2−2i222−222i2−2i20000−22−i2i2000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.