Finite Group Databasebeta

← Group #11775430

Character table — Group #11775430

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222244444444444448888888888161616161616161618182424242424242424242424242424242424242424242424243636367272
order122222334466666634666666612121212246612121212121266661212121244444488881212121212121212242424242424242444424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ311111111111111111111111111111111111111111111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1
χ511111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1
χ611111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1
χ711111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-111
χ811111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-111
χ91111-1-111-1-111111111-1-1111-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-111i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i1-1-1-11
χ101111-1-111-1-111111111-1-1111-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-111−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii1-1-1-11
χ111111-1-111-1-111111111-1-1111-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-1-1-1i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii-1111-1
χ121111-1-111-1-111111111-1-1111-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-1-1-1−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i-1111-1
χ131111-1-111-1-111111111-1-1111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1111111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii1-1-11-1
χ141111-1-111-1-111111111-1-1111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1111111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i1-1-11-1
χ151111-1-111-1-111111111-1-1111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i-111-11
χ161111-1-111-1-111111111-1-1111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-111-11
χ1722222222-2-22222222-22222222-2-2-2-20022-2-2-2-2-2-20000000022000000000000000000000000-2-2200
χ1822222222-2-22222222-22222222-2-2-2-20022-2-2-2-2-2-200000000-2-200000000000000000000000022-200
χ192222222-1222-122-1-1-122-1-1-1-12-122-1-122-1-12-1-1-1-1-12-1-1-12-1-1-100002200220000-1-1-1-10000-1-1-1-100000
χ202222222-1222-122-1-1-122-1-1-1-12-122-1-122-1-12-1-1-1-1-12-1-1-12-1-1-10000-2-200-2-2000011110000111100000
χ212222222-1222-122-1-1-122-1-1-1-12-122-1-1-2-2-1-12-1-1-1-1-1-2111-211100002200-2-20000-1-1-1-10000111100000
χ222222222-1222-122-1-1-122-1-1-1-12-122-1-1-2-2-1-12-1-1-1-1-1-2111-21110000-2-20022000011110000-1-1-1-100000
χ23222222-1222-12-1-122-12-12-1-1-1-12-1-12222-1-1-12-1-1-1-1-12-1-1-12-1-10022002200-1-1-1-10000-1-1-1-1000000000
χ24222222-1222-12-1-122-12-12-1-1-1-12-1-12222-1-1-12-1-1-1-1-12-1-1-12-1-100-2-200-2-200111100001111000000000
χ25222222-1222-12-1-122-12-12-1-1-1-12-1-122-2-2-1-1-12-1-1-1-11-2111-211002200-2-200-1-1-1-100001111000000000
χ26222222-1222-12-1-122-12-12-1-1-1-12-1-122-2-2-1-1-12-1-1-1-11-2111-21100-2-200220011110000-1-1-1-1000000000
χ272222-2-222222222222-2-2-2222-2-2222200-2-2-2-2-2-2220000000022000000000000000000000000-22-200
χ282222-2-222222222222-2-2-2222-2-2222200-2-2-2-2-2-22200000000-2-20000000000000000000000002-2200
χ292222-2-22-1-2-22-122-1-1-12-21-1-1-1-21-2-2112-2112-1-1-1112-1-1-1-211100002i−2i002i−2i0000−i−iii0000−i−iii00000
χ302222-2-22-1-2-22-122-1-1-12-21-1-1-1-21-2-2112-2112-1-1-1112-1-1-1-21110000−2i2i00−2i2i0000ii−i−i0000ii−i−i00000
χ312222-2-22-1-2-22-122-1-1-12-21-1-1-1-21-2-211-22112-1-1-111-21112-1-1-100002i−2i00−2i2i0000−i−iii0000ii−i−i00000
χ322222-2-22-1-2-22-122-1-1-12-21-1-1-1-21-2-211-22112-1-1-111-21112-1-1-10000−2i2i002i−2i0000ii−i−i0000−i−iii00000
χ332222-2-2-12-2-2-12-1-122-121-2-1-1-11-211-2-22-211-12-1-111-12-1-11-211002i−2i002i−2i00−i−iii0000−i−iii000000000
χ342222-2-2-12-2-2-12-1-122-121-2-1-1-11-211-2-22-211-12-1-111-12-1-11-21100−2i2i00−2i2i00ii−i−i0000ii−i−i000000000
χ352222-2-2-12-2-2-12-1-122-121-2-1-1-11-211-2-2-2211-12-1-1111-211-12-1-1002i−2i00−2i2i00−i−iii0000ii−i−i000000000
χ362222-2-2-12-2-2-12-1-122-121-2-1-1-11-211-2-2-2211-12-1-1111-211-12-1-100−2i2i002i−2i00ii−i−i0000−i−iii000000000
χ374444444-2-4-44-244-2-2-2-44-2-2-2-24-2-4-42200-2-2-422222000000000000000000000000000000000000000
χ38444444-24-4-4-24-2-244-2-4-24-2-2-2-2422-4-400-2-22-42222000000000000000000000000000000000000000
χ39444444-2-244-2-2-2-2-2-214-2-2111-2-2-2-2-2-24411-2-21111-2-211-2-2110000000000000000000000000000000
χ40444444-2-244-2-2-2-2-2-214-2-2111-2-2-2-2-2-2-4-411-2-2111122-1-122-1-10000000000000000000000000000000
χ41444444-2-2-4-4-2-2-2-2-2-21-4-2-2111-2-22222001122-1-1-1-1003-3003-30000000000000000000000000000000
χ42444444-2-2-4-4-2-2-2-2-2-21-4-2-2111-2-22222001122-1-1-1-100-3300-330000000000000000000000000000000
χ434444-4-44-2444-244-2-2-2-4-42-2-2-2-4244-2-20022-4222-2-2000000000000000000000000000000000000000
χ444444-4-4-2444-24-2-244-2-42-4-2-2-22-4-2-24400222-422-2-2000000000000000000000000000000000000000
χ454444-4-4-2-244-2-2-2-2-2-21-42211122-2-2-2-200-1-122-1-111003-300-330000000000000000000000000000000
χ464444-4-4-2-244-2-2-2-2-2-21-42211122-2-2-2-200-1-122-1-11100-33003-30000000000000000000000000000000
χ474444-4-4-2-2-4-4-2-2-2-2-2-214221112222224-4-1-1-2-211-1-1-2-21122-1-10000000000000000000000000000000
χ484444-4-4-2-2-4-4-2-2-2-2-2-21422111222222-44-1-1-2-211-1-122-1-1-2-2110000000000000000000000000000000
χ4944-4-4004400-4-44-44-44000-44-40000000000000000000000004i−4i00000000000000000000000000000
χ5044-4-4004400-4-44-44-44000-44-4000000000000000000000000−4i4i00000000000000000000000000000
χ514-44-400444i−4i44-4-4-4-440004-4-4004i−4i4i−4i000000004i−4i000000000000000000000000000000000000000
χ524-44-40044−4i4i44-4-4-4-440004-4-400−4i4i−4i4i00000000−4i4i000000000000000000000000000000000000000
χ534-44-4004-24i−4i4-2-4-422-2000-222004i−4i−2i2i00000000−2i2i0000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000
χ544-44-4004-24i−4i4-2-4-422-2000-222004i−4i−2i2i00000000−2i2i0000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000
χ554-44-4004-2−4i4i4-2-4-422-2000-22200−4i4i2i−2i000000002i−2i0000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000
χ564-44-4004-2−4i4i4-2-4-422-2000-22200−4i4i2i−2i000000002i−2i0000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000
χ574-44-400-244i−4i-2422-4-4-2000-22200−2i2i4i−4i00000000−2i2i000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000
χ584-44-400-244i−4i-2422-4-4-2000-22200−2i2i4i−4i00000000−2i2i000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000
χ594-44-400-24−4i4i-2422-4-4-2000-222002i−2i−4i4i000000002i−2i000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000
χ604-44-400-24−4i4i-2422-4-4-2000-222002i−2i−4i4i000000002i−2i000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000
χ614-4-444-44400-4-4-44-44404-4-4-44-440000004-4000000000000000000000000000000000000000000000
χ624-4-444-44-200-42-442-2-204222-2-4-2000000-22000000000000000000000000000000000000i6−i6i6−i600000
χ634-4-444-44-200-42-442-2-204222-2-4-2000000-22000000000000000000000000000000000000−i6i6−i6i600000
χ644-4-444-4-24002-42-2-44-20-2-422-224000000-22000000000000000000000000000000006−66−6000000000
χ654-4-444-4-24002-42-2-44-20-2-422-224000000-2200000000000000000000000000000000−66−66000000000
χ664-4-44-444400-4-4-44-4440-44-4-444-4000000-44000000000000000000000000000000000000000000000
χ674-4-44-444-200-42-442-2-20-4-222-2420000002-20000000000000000000000000000000000006−6−6600000
χ684-4-44-444-200-42-442-2-20-4-222-2420000002-2000000000000000000000000000000000000−666−600000
χ694-4-44-44-24002-42-2-44-202422-2-2-40000002-200000000000000000000000000000000i6−i6−i6i6000000000
χ704-4-44-44-24002-42-2-44-202422-2-2-40000002-200000000000000000000000000000000−i6i6i6−i6000000000
χ7188-8-8008-400-848-8-44-40004-440000000000000000000000000000000000000000000000000000000
χ7288-8-800-48004-8-448-8-40004-440000000000000000000000000000000000000000000000000000000
χ7388-8-800-4-40044-44-442000-22-20000000000006-600000000000000000000000000000000000000000
χ7488-8-800-4-40044-44-442000-22-2000000000000-6600000000000000000000000000000000000000000
χ758-88-800-4-48i−8i-4-4444420002-2-200−4i4i−4i4i000000002i−2i000000000000000000000000000000000000000
χ768-88-800-4-4−8i8i-4-4444420002-2-2004i−4i4i−4i00000000−2i2i000000000000000000000000000000000000000
χ778-8-888-8-4-400444-44-420-44-2-224-40000002-2000000000000000000000000000000000000000000000
χ788-8-88-88-4-400444-44-4204-4-2-22-44000000-22000000000000000000000000000000000000000000000

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