Finite Group Databasebeta

← Group #11775329

Character table — Group #11775329

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222444444444444444666666888888888888812121212121212121216161616161624242424242424242424242424242424242472727272
order1222223344666666346666666121212121212226666446612121212121212121224466121212121212121212124444881212121212121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111111-1-1111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111111-1-1
χ91111-1-111-1-111111111-1-1-1111-111-1-1-1-11111111-1-1-1111-1-111-1-1-11-1-1-111-1-11-111-1-11-1i−ii−i11-1-1ii−i−iii−i−ii−ii−i
χ101111-1-111-1-111111111-1-1-1111-111-1-1-1-11111111-1-1-1111-1-111-1-1-11-1-1-111-1-11-111-1-11-1−ii−ii11-1-1−i−iii−i−iii−ii−ii
χ111111-1-111-1-111111111-1-1-1111-111-1-1-1-1111111-11-1-11-1-11111-1-1-11-1-1-111-1-1-11-1-111-11i−i−ii-1-111ii−i−i−i−iiii−i−ii
χ121111-1-111-1-111111111-1-1-1111-111-1-1-1-1111111-11-1-11-1-11111-1-1-11-1-1-111-1-1-11-1-111-11−iii−i-1-111−i−iiiii−i−i−iii−i
χ131111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-11-1111-1-1111-111-1-1-11i−ii−i-1-111ii−i−iii−i−i−ii−ii
χ141111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-11-1111-1-1111-111-1-1-11−ii−ii-1-111−i−iii−i−iiii−ii−i
χ151111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11-1111-1-111-11-1-1111-1i−i−ii11-1-1ii−i−i−i−iii−iii−i
χ161111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11-1111-1-111-11-1-1111-1−iii−i11-1-1−i−iiiii−i−ii−i−ii
χ1722222222-2-22222222-22222222-2-2-2-2-2-22222220022-20000-2-2-2-22-2-222-2-2-2-20000000000000000000000000000
χ1822222222-2-22222222-22222222-2-2-2-2-2-2-2-2-2-2-2-20022-20000-2-2-2-2-222-2-222220000000000000000000000000000
χ192222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-12222-1-1-1-122-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1220000-1-1-1-1000000000000
χ202222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-12222-1-1-1-1-2-2-1-121111-1-1-1-1222-1-1-1-1-1-1-2-21111-2-200001111000000000000
χ212222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-122-2-2111122-1-12-1-1-1-1-1-1-1-1-2-2-211111122-1-1-1-1-2-200001111000000000000
χ222222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-122-2-21111-2-2-1-121111-1-1-1-1-2-2-2111111-2-21111220000-1-1-1-1000000000000
χ232222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-222-1-1-1-100-1-1-2−i3i3−i3i311112-2-2-1-1111100−i3i3−i3i3000000−i3i3−i3i3000000000000
χ242222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-222-1-1-1-100-1-1-2i3−i3i3−i311112-2-2-1-1111100i3−i3i3−i3000000i3−i3i3−i3000000000000
χ252222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-2-2-2111100-1-1-2−i3i3−i3i31111-22211-1-1-1-100−i3i3−i3i3000000i3−i3i3−i3000000000000
χ262222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-2-2-2111100-1-1-2i3−i3i3−i31111-22211-1-1-1-100i3−i3i3−i3000000−i3i3−i3i3000000000000
χ27222222-1222-12-1-122-12-122-1-1-1-12222-1-100000022-1-1-12222-1-1-1-1000000000-1-1-1-1-1-10022220000-1-1-1-1-1-1-1-10000
χ28222222-1222-12-1-122-12-122-1-1-1-12222-1-100000022-1-1-12222-1-1-1-1000000000-1-1-1-1-1-100-2-2-2-20000111111110000
χ29222222-1222-12-1-122-12-122-1-1-1-12222-1-1000000-2-2-1-1-1-2-2-2-2-1-1-1-10000000001111110022-2-20000-1-1-1-111110000
χ30222222-1222-12-1-122-12-122-1-1-1-12222-1-1000000-2-2-1-1-1-2-2-2-2-1-1-1-100000000011111100-2-22200001111-1-1-1-10000
χ312222-2-222222222222-2-2-2-2222-2-2-2222222222200-2-2-20000-2-222-2-22-2-2-2-2220000000000000000000000000000
χ322222-2-222222222222-2-2-2-2222-2-2-22222-2-2-2-2-2-200-2-2-20000-2-22222-22222-2-20000000000000000000000000000
χ332222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-12222-1-1-1-10011-2−i3i3i3−i311-1-1-2-221111-1-100−i3i3i3−i3000000−i3i3i3−i3000000000000
χ342222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-12222-1-1-1-10011-2i3−i3−i3i311-1-1-2-221111-1-100i3−i3−i3i3000000i3−i3−i3i3000000000000
χ352222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-122-2-211110011-2−i3i3i3−i311-1-122-2-1-1-1-11100−i3i3i3−i3000000i3−i3−i3i3000000000000
χ362222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-122-2-211110011-2i3−i3−i3i311-1-122-2-1-1-1-11100i3−i3−i3i3000000−i3i3i3−i3000000000000
χ372222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-222-1-1-1-12-2112-1-111-1-111-22-211-1-1112-2-1-1112-20000-1-111000000000000
χ382222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-222-1-1-1-1-2211211-1-1-1-111-22-211-1-111-2211-1-1-22000011-1-1000000000000
χ392222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-2-2-211112-2112-1-111-1-1112-22-1-111-1-12-2-1-111-22000011-1-1000000000000
χ402222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-2-2-21111-2211211-1-1-1-1112-22-1-111-1-1-2211-1-12-20000-1-111000000000000
χ412222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-2110000002-211-122-2-2-1-111000000000-11-1-111002i−2i2i−2i0000−i−iii−i−iii0000
χ422222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-2110000002-211-122-2-2-1-111000000000-11-1-11100−2i2i−2i2i0000ii−i−iii−i−i0000
χ432222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-211000000-2211-1-2-222-1-1110000000001-111-1-1002i−2i−2i2i0000−i−iiiii−i−i0000
χ442222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-211000000-2211-1-2-222-1-1110000000001-111-1-100−2i2i2i−2i0000ii−i−i−i−iii0000
χ45444444-24-4-4-24-2-244-2-4-244-2-2-2-2-4-4-4-42200000000-2-22000022220000000000000000000000000000000000000
χ46444444-2-244-2-2-2-2-2-214-2-2-2111-2-2-2-2-2-2-20000004411-2-2-2-2-21111000000000-2-211110000000000000000000000
χ47444444-2-244-2-2-2-2-2-214-2-2-2111-2-2-2-2-2-2-2000000-4-411-22222111100000000022-1-1-1-10000000000000000000000
χ48444444-2-2-4-4-2-2-2-2-2-21-4-2-2-2111-222222200000000112−2i32i3−2i32i3-1-1-1-100000000000i3−i3i3−i30000000000000000000000
χ49444444-2-2-4-4-2-2-2-2-2-21-4-2-2-2111-2222222000000001122i3−2i32i3−2i3-1-1-1-100000000000−i3i3−i3i30000000000000000000000
χ504444-4-4-2444-24-2-244-2-42-4-4-2-2-22-4-444-2-200000000222000022-2-20000000000000000000000000000000000000
χ514444-4-4-2-244-2-2-2-2-2-21-4222111222-2-2-2-200000000-1-12−2i32i32i3−2i3-1-11100000000000i3−i3−i3i30000000000000000000000
χ524444-4-4-2-244-2-2-2-2-2-21-4222111222-2-2-2-200000000-1-122i3−2i3−2i32i3-1-11100000000000−i3i3i3−i30000000000000000000000
χ534444-4-4-2-2-4-4-2-2-2-2-2-2142221112-2-222220000004-4-1-1-2-2-22211-1-1000000000-2211-1-10000000000000000000000
χ544444-4-4-2-2-4-4-2-2-2-2-2-2142221112-2-22222000000-44-1-1-222-2-211-1-10000000002-2-1-1110000000000000000000000
χ5544-4-44-4440044-4-4-4-440-44-44-4-44000000000000004-40000000000000000000000000000000000000000000000
χ5644-4-44-44-2004-2-4-422-20-4-22-222400000000−2i3−2i32i32i300-22000000000000−2i32i300000000000000000000000000000000
χ5744-4-44-44-2004-2-4-422-20-4-22-2224000000002i32i3−2i3−2i300-220000000000002i3−2i300000000000000000000000000000000
χ5844-4-44-4-2400-2422-4-4-2024-4-222-200000000000000-22000000000000000000000000000000000000006−66−60000
χ5944-4-44-4-2400-2422-4-4-2024-4-222-200000000000000-2200000000000000000000000000000000000000−66−660000
χ6044-4-4-44440044-4-4-4-4404-444-4-4-400000000000000-440000000000000000000000000000000000000000000000
χ6144-4-4-444-2004-2-4-422-2042-2-222-400000000−2i3−2i32i32i3002-20000000000002i3−2i300000000000000000000000000000000
χ6244-4-4-444-2004-2-4-422-2042-2-222-4000000002i32i3−2i3−2i3002-2000000000000−2i32i300000000000000000000000000000000
χ6344-4-4-44-2400-2422-4-4-20-2-44-2222000000000000002-200000000000000000000000000000000000000i6−i6−i6i60000
χ6444-4-4-44-2400-2422-4-4-20-2-44-2222000000000000002-200000000000000000000000000000000000000−i6i6i6−i60000
χ654-44-400444i−4i-4-44-44-440000-44-40004i−4i4i−4i000000000000000004i−4i0000000000000000000000000000000000000
χ664-44-40044−4i4i-4-44-44-440000-44-4000−4i4i−4i4i00000000000000000−4i4i0000000000000000000000000000000000000
χ674-44-4004-24i−4i-424-4-22-200002-22000−2i2i4i−4i00−2i32i3−2i32i300000000000−2i2i000000023−230000000000000000000000000000
χ684-44-4004-24i−4i-424-4-22-200002-22000−2i2i4i−4i002i3−2i32i3−2i300000000000−2i2i0000000−23230000000000000000000000000000
χ694-44-4004-2−4i4i-424-4-22-200002-220002i−2i−4i4i00−2i32i3−2i32i3000000000002i−2i0000000−23230000000000000000000000000000
χ704-44-4004-2−4i4i-424-4-22-200002-220002i−2i−4i4i002i3−2i32i3−2i3000000000002i−2i000000023−230000000000000000000000000000
χ714-44-400-244i−4i2-4-224-4-200002-220004i−4i−2i2i00000000000000000−2i2i0000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000
χ724-44-400-244i−4i2-4-224-4-200002-220004i−4i−2i2i00000000000000000−2i2i0000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000
χ734-44-400-24−4i4i2-4-224-4-200002-22000−4i4i2i−2i000000000000000002i−2i0000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000
χ744-44-400-24−4i4i2-4-224-4-200002-22000−4i4i2i−2i000000000000000002i−2i0000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000
χ754-4-44004400-4-4-44-4440000-4-4400000004-44-4-4400000000000000000000000000000000000000000000000000
χ764-4-44004400-4-4-44-4440000-4-440000000-44-444-400000000000000000000000000000000000000000000000000
χ774-4-44004-200-42-442-2-2000022-20−2i32i300004-4-222-2000000000−2i32i30000000−2i32i3000000000000000000000000000000
χ784-4-44004-200-42-442-2-2000022-20−2i32i30000-442-2-22000000000−2i32i300000002i3−2i3000000000000000000000000000000
χ794-4-44004-200-42-442-2-2000022-202i3−2i300004-4-222-20000000002i3−2i300000002i3−2i3000000000000000000000000000000
χ804-4-44004-200-42-442-2-2000022-202i3−2i30000-442-2-220000000002i3−2i30000000−2i32i3000000000000000000000000000000
χ8188-8-88-8-4-400-4-44444204-442-2-2-4000000000000002-20000000000000000000000000000000000000000000000
χ8288-8-8-88-4-400-4-4444420-44-42-2-2400000000000000-220000000000000000000000000000000000000000000000
χ838-88-800-4-48i−8i44-44-4420000-22-2000−4i4i−4i4i000000000000000002i−2i0000000000000000000000000000000000000
χ848-88-800-4-4−8i8i44-44-4420000-22-20004i−4i4i−4i00000000000000000−2i2i0000000000000000000000000000000000000
χ858-8-8800-48004-84-4-88-4000044-4000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-400444-44-420000-2-220−4i34i300000000000000000002i3−2i3000000000000000000000000000000000000000
χ878-8-8800-4-400444-44-420000-2-2204i3−4i30000000000000000000−2i32i3000000000000000000000000000000000000000

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