Finite Group Databasebeta

← Group #11778521

Character table — Group #11778521

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order122222336666666666344446666666661212121241212121212121212121212121212121212121212121244448888121212121212121224242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11-1-11
χ61111111111111111111-1-1111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1
χ71111111111111111111-1-1111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-111-1
χ81111111111111111111-1-1111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-11
χ9222222222222222222222-2-2222222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ102222222222222222222-2-2-2-2222222222-2-2-2-2222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ112222222-1222-1-12-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ122222222-1222-1-12-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ132222222-1222-1-12-1222-122-2-2-1-1-1-1-1-1-1-1-11111-211-2-222-1-1-2-211111111-1-1-1-1000000000000000033−3−333−3−30000
χ142222222-1222-1-12-1222-122-2-2-1-1-1-1-1-1-1-1-11111-211-2-222-1-1-2-211111111-1-1-1-10000000000000000−3−333−3−3330000
χ152222222-1222-1-12-1222-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-21122-2-211-2-21111-1-1-1-11111000022-2-200000000-1-1-1-111110000
χ162222222-1222-1-12-1222-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-21122-2-211-2-21111-1-1-1-111110000-2-222000000001111-1-1-1-10000
χ172222222-1222-1-12-1222-1-2-2-2-2-1-1-1-1-1-1-1-1-111112-1-1-2-2-2-21122-1-1-1-111111111000000000000000033−3−3−3−3330000
χ182222222-1222-1-12-1222-1-2-2-2-2-1-1-1-1-1-1-1-1-111112-1-1-2-2-2-21122-1-1-1-1111111110000000000000000−3−33333−3−30000
χ19222222-12-1-1-122-12-1-1-1-1222222-1-1-1-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ20222222-12-1-1-122-12-1-1-1-1222222-1-1-1-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ21222222-12-1-1-122-12-1-1-1-122-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-211-1-1221111111111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ22222222-12-1-1-122-12-1-1-1-122-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-211-1-1221111111111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ23222222-12-1-1-122-12-1-1-1-1-2-22222-1-1-1-1-1-1-12222-2-2-2-1-111-2-2111111-1-1-1-1111122-2-200001111-1-1-1-1000000000000
χ24222222-12-1-1-122-12-1-1-1-1-2-22222-1-1-1-1-1-1-12222-2-2-2-1-111-2-2111111-1-1-1-11111-2-2220000-1-1-1-11111000000000000
χ25222222-12-1-1-122-12-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22221111-2-2-1-1-1-1-1-11111111100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ26222222-12-1-1-122-12-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22221111-2-2-1-1-1-1-1-11111111100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ272222-2-2222-2-22222-2-222002-2-2-22-2-2-2-22222-2-20002-2000000000022-2-20000000000000000000000000000200-2
χ282222-2-2222-2-22222-2-222002-2-2-22-2-2-2-22222-2-20002-2000000000022-2-20000000000000000000000000000-2002
χ292222-2-2222-2-22222-2-22200-22-2-22-2-2-2-222-2-222000-220000000000-2-222000000000000000000000000000002-20
χ302222-2-2222-2-22222-2-22200-22-2-22-2-2-2-222-2-222000-220000000000-2-22200000000000000000000000000000-220
χ312-2-222-222-222-22-2-2-2-2222i−2i002-2-222-2-22-20000000002i−2i2i−2i00000000002i2i−2i−2i00002−2−i2i2000000002−22−2−i2i2−i2i20000
χ322-2-222-222-222-22-2-2-2-2222i−2i002-2-222-2-22-20000000002i−2i2i−2i00000000002i2i−2i−2i0000−22i2−i200000000−22−22i2−i2i2−i20000
χ332-2-222-222-222-22-2-2-2-222−2i2i002-2-222-2-22-2000000000−2i2i−2i2i0000000000−2i−2i2i2i00002−2i2−i2000000002−22−2i2−i2i2−i20000
χ342-2-222-222-222-22-2-2-2-222−2i2i002-2-222-2-22-2000000000−2i2i−2i2i0000000000−2i−2i2i2i0000−22−i2i200000000−22−22−i2i2−i2i20000
χ352-2-222-22-1-2221-1-21-2-22-12i−2i00-111-1-111-113−33−30−i3i3002i−2i−ii00−i3−i3i3i33−33−3−i−iii00002−2−i2i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ362-2-222-22-1-2221-1-21-2-22-12i−2i00-111-1-111-113−33−30−i3i3002i−2i−ii00−i3−i3i3i33−33−3−i−iii0000−22i2−i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ372-2-222-22-1-2221-1-21-2-22-12i−2i00-111-1-111-11−33−330i3−i3002i−2i−ii00i3i3−i3−i3−33−33−i−iii00002−2−i2i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ382-2-222-22-1-2221-1-21-2-22-12i−2i00-111-1-111-11−33−330i3−i3002i−2i−ii00i3i3−i3−i3−33−33−i−iii0000−22i2−i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ392-2-222-22-1-2221-1-21-2-22-1−2i2i00-111-1-111-113−33−30i3−i300−2i2ii−i00i3i3−i3−i33−33−3ii−i−i00002−2i2−i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ402-2-222-22-1-2221-1-21-2-22-1−2i2i00-111-1-111-113−33−30i3−i300−2i2ii−i00i3i3−i3−i33−33−3ii−i−i0000−22−i2i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ412-2-222-22-1-2221-1-21-2-22-1−2i2i00-111-1-111-11−33−330−i3i300−2i2ii−i00−i3−i3i3i3−33−33ii−i−i00002−2i2−i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ422-2-222-22-1-2221-1-21-2-22-1−2i2i00-111-1-111-11−33−330−i3i300−2i2ii−i00−i3−i3i3i3−33−33ii−i−i0000−22−i2i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ43444444-2-2-2-2-2-2-2-2-2-2-2-214444-2-21111111-2-2-2-24-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2144-4-4-2-211111112222-42222-2-2-2-222-1-1-1-1-1-1-1-111110000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-21-4-444-2-21111111-2-2-2-2-422-2-2222222-1-1-1-11111-1-1-1-10000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-4-4-2-2111111122224-2-2222222-2-21111-1-1-1-1-1-1-1-10000000000000000000000000000
χ474444-4-44-24-4-4-2-24-2-4-44-2004-422-22222-2-2-2-2220004-40000000000-2-22200000000000000000000000000000000
χ484444-4-44-24-4-4-2-24-2-4-44-200-4422-22222-2-222-2-2000-44000000000022-2-200000000000000000000000000000000
χ494444-4-4-24-22244-2422-2-2004-4-4-4-22222-2-244-4-4000-220000000000-2-22200000000000000000000000000000000
χ504444-4-4-24-22244-2422-2-200-44-4-4-22222-2-2-4-4440002-2000000000022-2-200000000000000000000000000000000
χ514444-4-4-2-2-222-2-2-2-222-21004-4221-1-1-1-111-2-222000-220000003-33-311-1-13-33-30000000000000000000000000000
χ524444-4-4-2-2-222-2-2-2-222-21004-4221-1-1-1-111-2-222000-22000000-33-3311-1-1-33-330000000000000000000000000000
χ534444-4-4-2-2-222-2-2-2-222-2100-44221-1-1-1-11122-2-20002-20000003-33-3-1-111-33-330000000000000000000000000000
χ544444-4-4-2-2-222-2-2-2-222-2100-44221-1-1-1-11122-2-20002-2000000-33-33-1-1113-33-30000000000000000000000000000
χ5544-4-400444004-4-4-400-4400000040000-4-4000000000000000000000000000002-200002-22-20000000000000000
χ5644-4-400444004-4-4-400-4400000040000-4-400000000000000000000000000000-220000-22-220000000000000000
χ5744-4-400-24-2−2i32i34-42-4−2i32i32-2000000-2−2i32i3−2i32i322000000000000000000000000000002-20000−1−i31+i3−1+i31−i30000000000000000
χ5844-4-400-24-2−2i32i34-42-4−2i32i32-2000000-2−2i32i3−2i32i32200000000000000000000000000000-2200001+i3−1−i31−i3−1+i30000000000000000
χ5944-4-400-24-22i3−2i34-42-42i3−2i32-2000000-22i3−2i32i3−2i322000000000000000000000000000002-20000−1+i31−i3−1−i31+i30000000000000000
χ6044-4-400-24-22i3−2i34-42-42i3−2i32-2000000-22i3−2i32i3−2i32200000000000000000000000000000-2200001−i3−1+i31+i3−1−i30000000000000000
χ614-44-40044-400-4-44400-44000000-40000-440000000000000000000000000002i−2i00000000002i−2i2i−2i000000000000
χ624-44-40044-400-4-44400-44000000-40000-44000000000000000000000000000−2i2i0000000000−2i2i−2i2i000000000000
χ634-44-400-242−2i32i3-4-4-242i3−2i32-20000002−2i32i32i3−2i32-20000000000000000000000000002i−2i00000000002ζ22−2ζ222ζ14−2ζ14000000000000
χ644-44-400-242−2i32i3-4-4-242i3−2i32-20000002−2i32i32i3−2i32-2000000000000000000000000000−2i2i0000000000−2ζ222ζ22−2ζ142ζ14000000000000
χ654-44-400-2422i3−2i3-4-4-24−2i32i32-200000022i3−2i3−2i32i32-20000000000000000000000000002i−2i00000000002ζ14−2ζ142ζ22−2ζ22000000000000
χ664-44-400-2422i3−2i3-4-4-24−2i32i32-200000022i3−2i3−2i32i32-2000000000000000000000000000−2i2i0000000000−2ζ142ζ14−2ζ222ζ22000000000000
χ674-4-444-4-242-2-2-442-422-2-24i−4i004-42-2-222-22000000000−2i2i4i−4i0000000000−2i−2i2i2i0000000000000000000000000000
χ684-4-444-4-242-2-2-442-422-2-2−4i4i004-42-2-222-220000000002i−2i−4i4i00000000002i2i−2i−2i0000000000000000000000000000
χ694-4-444-4-2-22-2-22-22222-214i−4i00-22-111-1-11-123−2323−230−2i32i300−2i2i−2i2i00i3i3−i3−i3−33−33ii−i−i0000000000000000000000000000
χ704-4-444-4-2-22-2-22-22222-214i−4i00-22-111-1-11-1−2323−232302i3−2i300−2i2i−2i2i00−i3−i3i3i33−33−3ii−i−i0000000000000000000000000000
χ714-4-444-4-2-22-2-22-22222-21−4i4i00-22-111-1-11-123−2323−2302i3−2i3002i−2i2i−2i00−i3−i3i3i3−33−33−i−iii0000000000000000000000000000
χ724-4-444-4-2-22-2-22-22222-21−4i4i00-22-111-1-11-1−2323−23230−2i32i3002i−2i2i−2i00i3i3−i3−i33−33−3−i−iii0000000000000000000000000000
χ734-4-44-4444-4-4-4-44-4-444440000-44-4-4-4444-40000000000000000000000000000000000000000000000000000000
χ744-4-44-444-2-4-4-42-2-42444-200002-2222-2-2-2223−23−232300000000000000023−23−232300000000000000000000000000000000
χ754-4-44-444-2-4-4-42-2-42444-200002-2222-2-2-22−232323−23000000000000000−232323−2300000000000000000000000000000000
χ764-4-44-44-24222-442-4-2-2-2-20000-44222-2-2-220000000000000−2i32i3−2i32i32i3−2i3000000000000000000000000000000000000
χ774-4-44-44-24222-442-4-2-2-2-20000-44222-2-2-2200000000000002i3−2i32i3−2i3−2i32i3000000000000000000000000000000000000
χ784-4-44-44-2-22222-222-2-2-2100002-2-1-1-1111-123−23−2323000000000−2i32i3i3−i3−i3i3−333−3−3i3i3i−3i0000000000000000000000000000
χ794-4-44-44-2-22222-222-2-2-2100002-2-1-1-1111-123−23−23230000000002i3−2i3−i3i3i3−i3−333−33i−3i−3i3i0000000000000000000000000000
χ804-4-44-44-2-22222-222-2-2-2100002-2-1-1-1111-1−232323−23000000000−2i32i3i3−i3−i3i33−3−333i−3i−3i3i0000000000000000000000000000
χ814-4-44-44-2-22222-222-2-2-2100002-2-1-1-1111-1−232323−230000000002i3−2i3−i3i3i3−i33−3−33−3i3i3i−3i0000000000000000000000000000
χ8288-8-8008-4800-44-8400-8-4000000-40000440000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4-4−4i34i3-4444−4i34i34200000022i3−2i32i3−2i3-2-20000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-4-44i3−4i3-44444i3−4i3420000002−2i32i3−2i32i3-2-20000000000000000000000000000000000000000000000000000000
χ858-88-8008-4-800448-400-8-4000000400004-40000000000000000000000000000000000000000000000000000000
χ868-88-800-4-44−4i34i344-4-44i3−4i342000000-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000
χ878-88-800-4-444i3−4i344-4-4−4i34i342000000-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000

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