Finite Group Databasebeta

← Group #11775608

Character table — Group #11775608

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222244444444444444466666666668888888888888121212121212121212121216161616161624242424242424242424242424242424363636367272
order1222223344666666346666666121212121212222244666644661212121212121212124668888121212121212121212124444121212121212121224242424888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111111-1-1111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-11111-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ91111-1-111-1-111111111-1-1-1111-111-1-1-1-111-1-11111111-1-1-1111-1-111-1-1-1-1-1ii−i−i11-1-11-111-1-11-1i−i11-1-1ii−i−iii−i−iii−i−ii−i
χ101111-1-111-1-111111111-1-1-1111-111-1-1-1-111-1-11111111-1-1-1111-1-111-1-1-1-1-1−i−iii11-1-11-111-1-11-1−ii11-1-1−i−iii−i−iii−i−iii−ii
χ111111-1-111-1-111111111-1-1-1111-111-1-1-1-111-1-1111111-11-1-11-1-11111-1-1-1-1-1ii−i−i11-1-1-11-1-111-11−ii-1-111−i−iiiii−i−iii−i−i−ii
χ121111-1-111-1-111111111-1-1-1111-111-1-1-1-111-1-1111111-11-1-11-1-11111-1-1-1-1-1−i−iii11-1-1-11-1-111-11i−i-1-111ii−i−i−i−iii−i−iiii−i
χ131111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1111-1-111-1-1111ii−i−i-1-1111-111-1-1-11i−i-1-111ii−i−iii−i−i−i−iii−ii
χ141111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1111-1-111-1-1111−i−iii-1-1111-111-1-1-11−ii-1-111−i−iii−i−iiiii−i−ii−i
χ151111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-11-1-11111-1-1111ii−i−i-1-111-11-1-1111-1−ii11-1-1−i−iiiii−i−i−i−iiii−i
χ161111-1-111-1-111111111-1-1-1111-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-11-1-11111-1-1111−i−iii-1-111-11-1-1111-1i−i11-1-1ii−i−i−i−iiiii−i−i−ii
χ1722222222-2-22222222-22222222-2-2-2-2-2-22222-2-222220022-20000-2-2-2-2-2220000-2-2-2-20000000000000000000000000000
χ1822222222-2-22222222-22222222-2-2-2-2-2-2-2-2-2-222-2-2-2-20022-20000-2-2-2-22-2-2000022220000000000000000000000000000
χ192222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-122222222-1-1-1-122-1-12-1-1-1-1-1-1-1-12-1-10000-1-1-1-122-1-1-1-12200-1-1-1-100000000000000
χ202222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-122222222-1-1-1-1-2-2-1-121111-1-1-1-12-1-10000-1-1-1-1-2-21111-2-200111100000000000000
χ212222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-122-2-2-2-2-2-2111122-1-12-1-1-1-1-1-1-1-1-2110000111122-1-1-1-1-2-200111100000000000000
χ222222222-1222-122-1-1-122-1-1-1-1-12-1-1-1-122-2-2-2-2-2-21111-2-2-1-121111-1-1-1-1-21100001111-2-211112200-1-1-1-100000000000000
χ232222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-22222-2-2-1-1-1-100-1-1-2−i3i3−i3i31111-2-1-10000111100−i3i3−i3i30000−i3i3−i3i300000000000000
χ242222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-22222-2-2-1-1-1-100-1-1-2i3−i3i3−i31111-2-1-10000111100i3−i3i3−i30000i3−i3i3−i300000000000000
χ252222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-2-2-2-2-222111100-1-1-2−i3i3−i3i311112110000-1-1-1-100−i3i3−i3i30000i3−i3i3−i300000000000000
χ262222222-1-2-22-122-1-1-1-22-1-1-1-1-121111-2-2-2-2-2-222111100-1-1-2i3−i3i3−i311112110000-1-1-1-100i3−i3i3−i30000−i3i3−i3i300000000000000
χ27222222-1222-12-1-122-12-122-1-1-1-12222-1-1000000000022-1-1-12222-1-1-1-100022220000-1-1-1-1-1-100220000-1-1-1-1-1-1-1-1000000
χ28222222-1222-12-1-122-12-122-1-1-1-12222-1-1000000000022-1-1-12222-1-1-1-1000-2-2-2-20000-1-1-1-1-1-100-2-2000011111111000000
χ29222222-1222-12-1-122-12-122-1-1-1-12222-1-10000000000-2-2-1-1-1-2-2-2-2-1-1-1-10002222000011111100-2-200001111-1-1-1-1000000
χ30222222-1222-12-1-122-12-122-1-1-1-12222-1-10000000000-2-2-1-1-1-2-2-2-2-1-1-1-1000-2-2-2-2000011111100220000-1-1-1-11111000000
χ312222-2-222222222222-2-2-2-2222-2-2-2222222-2-2-2-2222200-2-2-20000-2-2222-2-20000-2-2220000000000000000000000000000
χ322222-2-222222222222-2-2-2-2222-2-2-22222-2-22222-2-2-2-200-2-2-20000-2-222-222000022-2-20000000000000000000000000000
χ332222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-12222-2-2-2-2-1-1-1-10011-2−i3i3i3−i311-1-1211000011-1-100−i3i3i3−i30000−i3i3i3−i300000000000000
χ342222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-12222-2-2-2-2-1-1-1-10011-2i3−i3−i3i311-1-1211000011-1-100i3−i3−i3i30000i3−i3−i3i300000000000000
χ352222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-122-2-2222211110011-2−i3i3i3−i311-1-1-2-1-10000-1-11100−i3i3i3−i30000i3−i3−i3i300000000000000
χ362222-2-22-1222-122-1-1-1-2-211-1-1-1-211-1-122-2-2222211110011-2i3−i3−i3i311-1-1-2-1-10000-1-11100i3−i3−i3i30000−i3i3i3−i300000000000000
χ372222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-222-2-222-1-1-1-12-2112-1-111-1-111-2110000-1-1112-2-1-1112-200-1-11100000000000000
χ382222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-222-2-222-1-1-1-1-2211211-1-1-1-111-2110000-1-111-2211-1-1-220011-1-100000000000000
χ392222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-2-2-222-2-211112-2112-1-111-1-1112-1-1000011-1-12-2-1-111-220011-1-100000000000000
χ402222-2-22-1-2-22-122-1-1-12-211-1-1-1-2-1-111-2-2-2-222-2-21111-2211211-1-1-1-1112-1-1000011-1-1-2211-1-12-200-1-11100000000000000
χ412222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-21100000000002-211-122-2-2-1-1110002i2i−2i−2i0000-11-1-111002i−2i0000−i−iii−i−iii000000
χ422222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-21100000000002-211-122-2-2-1-111000−2i−2i2i2i0000-11-1-11100−2i2i0000ii−i−iii−i−i000000
χ432222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-2110000000000-2211-1-2-222-1-1110002i2i−2i−2i00001-111-1-100−2i2i0000ii−i−i−i−iii000000
χ442222-2-2-12-2-2-12-1-122-121-2-2-1-1-1122-2-2110000000000-2211-1-2-222-1-111000−2i−2i2i2i00001-111-1-1002i−2i0000−i−iiiii−i−i000000
χ4522-2-22-2220022-2-2-2-22022-22-2-2-20000002-22-20022-2-2002-200000000002-22−22−200000000000000000000002−22−22−22−200
χ4622-2-22-2220022-2-2-2-22022-22-2-2-20000002-22-20022-2-2002-200000000002-2−22−220000000000000000000000−22−22−22−2200
χ4722-2-22-2220022-2-2-2-22022-22-2-2-2000000-22-2200-2-222002-20000000000-222−22−200000000000000000000002−22−2−22−2200
χ4822-2-22-2220022-2-2-2-22022-22-2-2-2000000-22-2200-2-222002-20000000000-22−22−220000000000000000000000−22−222−22−200
χ4922-2-2-22220022-2-2-2-220-2-222-2-220000002-2-220022-2-200-220000000000-22−i2i2i2−i20000000000000000000000−i2i2i2−i2−i2i2i2−i200
χ5022-2-2-22220022-2-2-2-220-2-222-2-220000002-2-220022-2-200-220000000000-22i2−i2−i2i20000000000000000000000i2−i2−i2i2i2−i2−i2i200
χ5122-2-2-22220022-2-2-2-220-2-222-2-22000000-222-200-2-22200-2200000000002-2−i2i2i2−i20000000000000000000000−i2i2i2−i2i2−i2−i2i200
χ5222-2-2-22220022-2-2-2-220-2-222-2-22000000-222-200-2-22200-2200000000002-2i2−i2−i2i20000000000000000000000i2−i2−i2i2−i2i2i2−i200
χ53444444-24-4-4-24-2-244-2-4-244-2-2-2-2-4-4-4-422000000000000-2-2200002222000000000000000000000000000000000000000
χ54444444-2-244-2-2-2-2-2-214-2-2-2111-2-2-2-2-2-2-200000000004411-2-2-2-2-2111100000000000-2-211110000000000000000000000
χ55444444-2-244-2-2-2-2-2-214-2-2-2111-2-2-2-2-2-2-20000000000-4-411-2222211110000000000022-1-1-1-10000000000000000000000
χ56444444-2-2-4-4-2-2-2-2-2-21-4-2-2-2111-2222222000000000000112−2i32i3−2i32i3-1-1-1-10000000000000i3−i3i3−i30000000000000000000000
χ57444444-2-2-4-4-2-2-2-2-2-21-4-2-2-2111-22222220000000000001122i3−2i32i3−2i3-1-1-1-10000000000000−i3i3−i3i30000000000000000000000
χ584444-4-4-2444-24-2-244-2-42-4-4-2-2-22-4-444-2-2000000000000222000022-2-2000000000000000000000000000000000000000
χ594444-4-4-2-244-2-2-2-2-2-21-4222111222-2-2-2-2000000000000-1-12−2i32i32i3−2i3-1-1110000000000000i3−i3−i3i30000000000000000000000
χ604444-4-4-2-244-2-2-2-2-2-21-4222111222-2-2-2-2000000000000-1-122i3−2i3−2i32i3-1-1110000000000000−i3i3i3−i30000000000000000000000
χ614444-4-4-2-2-4-4-2-2-2-2-2-2142221112-2-2222200000000004-4-1-1-2-2-22211-1-100000000000-2211-1-10000000000000000000000
χ624444-4-4-2-2-4-4-2-2-2-2-2-2142221112-2-222220000000000-44-1-1-222-2-211-1-1000000000002-2-1-1110000000000000000000000
χ6344-4-44-44-2004-2-4-422-204-22-222-40000004-44-400-2-22200-220000000000-22000000000000000000000000000000000000
χ6444-4-44-44-2004-2-4-422-204-22-222-4000000-44-440022-2-200-2200000000002-2000000000000000000000000000000000000
χ6544-4-44-4-2400-2422-4-4-20-24-4-2222000000000000000000-2200000000000022−2222−220000000000000000000000−22−22000000
χ6644-4-44-4-2400-2422-4-4-20-24-4-2222000000000000000000-22000000000000−2222−222200000000000000000000002−22−2000000
χ6744-4-4-444-2004-2-4-422-20-42-2-22240000004-4-4400-2-222002-200000000002-2000000000000000000000000000000000000
χ6844-4-4-444-2004-2-4-422-20-42-2-2224000000-444-40022-2-2002-20000000000-22000000000000000000000000000000000000
χ6944-4-4-44-2400-2422-4-4-202-44-222-20000000000000000002-2000000000000−2i22i22i2−2i20000000000000000000000i2−i2−i2i2000000
χ7044-4-4-44-2400-2422-4-4-202-44-222-20000000000000000002-20000000000002i2−2i2−2i22i20000000000000000000000−i2i2i2−i2000000
χ714-44-400444i−4i-4-44-44-440000-44-40004i−4i4i−4i0000000000000000000004i−4i000000000000000000000000000000000000000
χ724-44-40044−4i4i-4-44-44-440000-44-4000−4i4i−4i4i000000000000000000000−4i4i000000000000000000000000000000000000000
χ734-44-4004-24i−4i-424-4-22-200002-22000−2i2i4i−4i000000−2i32i3−2i32i300000000000−2i2i00000000023−230000000000000000000000000000
χ744-44-4004-24i−4i-424-4-22-200002-22000−2i2i4i−4i0000002i3−2i32i3−2i300000000000−2i2i000000000−23230000000000000000000000000000
χ754-44-4004-2−4i4i-424-4-22-200002-220002i−2i−4i4i000000−2i32i3−2i32i3000000000002i−2i000000000−23230000000000000000000000000000
χ764-44-4004-2−4i4i-424-4-22-200002-220002i−2i−4i4i0000002i3−2i32i3−2i3000000000002i−2i00000000023−230000000000000000000000000000
χ774-44-400-244i−4i2-4-224-4-200002-220004i−4i−2i2i000000000000000000000−2i2i0000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000
χ784-44-400-244i−4i2-4-224-4-200002-220004i−4i−2i2i000000000000000000000−2i2i0000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000
χ794-44-400-24−4i4i2-4-224-4-200002-22000−4i4i2i−2i0000000000000000000002i−2i0000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000
χ804-44-400-24−4i4i2-4-224-4-200002-22000−4i4i2i−2i0000000000000000000002i−2i0000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000
χ814-4-44004400-4-4-44-4440000-4-44000000000004-40000000000000000000000004-4000000000000000000000000000000
χ824-4-44004400-4-4-44-4440000-4-4400000000000-44000000000000000000000000-44000000000000000000000000000000
χ834-4-44004-200-42-442-2-2000022-20−2i32i3000000004-4−2i32i32i3−2i3000000000−2i32i3000000000-22000000000000000000000000000000
χ844-4-44004-200-42-442-2-2000022-20−2i32i300000000-442i3−2i3−2i32i3000000000−2i32i30000000002-2000000000000000000000000000000
χ854-4-44004-200-42-442-2-2000022-202i3−2i3000000004-42i3−2i3−2i32i30000000002i3−2i3000000000-22000000000000000000000000000000
χ864-4-44004-200-42-442-2-2000022-202i3−2i300000000-44−2i32i32i3−2i30000000002i3−2i30000000002-2000000000000000000000000000000
χ8788-8-88-8-4-400-4-4444420-4-442-2-240000000000000000002-2000000000000000000000000000000000000000000000000
χ8888-8-8-88-4-400-4-444442044-42-2-2-4000000000000000000-22000000000000000000000000000000000000000000000000
χ898-88-800-4-48i−8i44-44-4420000-22-2000−4i4i−4i4i0000000000000000000002i−2i000000000000000000000000000000000000000
χ908-88-800-4-4−8i8i44-44-4420000-22-20004i−4i4i−4i000000000000000000000−2i2i000000000000000000000000000000000000000
χ918-8-8800-48004-84-4-88-4000044-4000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800-4-400444-44-420000-2-220−4i34i3000000000000000000000002i3−2i300000000000000000000000000000000000000000
χ938-8-8800-4-400444-44-420000-2-2204i3−4i300000000000000000000000−2i32i300000000000000000000000000000000000000000

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