Finite Group Databasebeta

← Group #11775435

Character table — Group #11775435

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444444444888888888888888888888888181824242424242424242424242424242424363636484848487272
order12222233446666663466666661212121212121212668812121212242424242424242424242424242424244422444444121212121212121244466121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111
χ3111111111111111111111111111111111111111111111111111111111-1-11-11-111-1-11111-1-1-1-1-1-1-11-11-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-11-11-1-111-1-1-1-11111-1-1-1-11-11-1-1
χ511111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1
χ611111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1
χ711111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11111-1-1-11-11-111
χ811111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-1-1-11-1111
χ91111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i111-1-11i−ii−iii−i−iii−i−i1-1-11-1-11i−i
χ101111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i11-111-1−ii−ii−i−iii−i−iii1-1-1-111-1i−i
χ111111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1i−i−iiii−i−i−i−iii-11111-1-1−ii
χ121111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111−iii−i−i−iiiii−i−i-111-1-111−ii
χ131111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii111-1-11−ii−ii−i−iii−i−iii1-1-11-1-11−ii
χ141111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii11-111-1i−ii−iii−i−iii−i−i1-1-1-111-1−ii
χ151111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1−iii−i−i−iiiii−i−i-11111-1-1i−i
χ161111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111i−i−iiii−i−i−i−iii-111-1-111i−i
χ1722222222-2-22222222-22222222-2-2-2-2-2-2-2-22200-2-2-2-20000000000000000220000000000000000-2-22000000
χ1822222222-2-22222222-22222222-2-2-2-2-2-2-2-22200-2-2-2-20000000000000000-2-2000000000000000022-2000000
χ192222222-1222-12-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100020200220000-1-1-1-10000-10-100
χ202222222-1222-12-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000-20-200-2-200001111000010100
χ212222222-1222-12-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2111111-2-211111100020200-2-2000011110000-10-100
χ222222222-1222-12-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2111111-2-2111111000-20-200220000-1-1-1-1000010100
χ23222222-1222-12-12-12-12-12-1-1-1-12-1-122-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10020202200-1-1-1-10000000-10-1000
χ24222222-1222-12-12-12-12-12-1-1-1-12-1-122-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100-20-20-2-20011110000000101000
χ25222222-1222-12-12-12-12-12-1-1-1-12-1-122-1-1-1-1-1-1-2-2-12-1-111-2-2111111-2-21111002020-2-20011110000000-10-1000
χ26222222-1222-12-12-12-12-12-1-1-1-12-1-122-1-1-1-1-1-1-2-2-12-1-111-2-2111111-2-2111100-20-202200-1-1-1-10000000101000
χ272222-2-222222222222-2-2-2222-2-222222222-2-200-2-2-2-20000000000000000220000000000000000-22-2000000
χ282222-2-222222222222-2-2-2222-2-222222222-2-200-2-2-2-20000000000000000-2-200000000000000002-22000000
χ292222-2-22-1-2-22-12-12-1-12-21-1-1-1-21-2-2111111112i−2i2-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii00020-200−2i2i0000ii−i−i0000-10100
χ302222-2-22-1-2-22-12-12-1-12-21-1-1-1-21-2-2111111112i−2i2-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii000-202002i−2i0000−i−iii000010-100
χ312222-2-22-1-2-22-12-12-1-12-21-1-1-1-21-2-211111111−2i2i2-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i00020-2002i−2i0000−i−iii0000-10100
χ322222-2-22-1-2-22-12-12-1-12-21-1-1-1-21-2-211111111−2i2i2-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i000-20200−2i2i0000ii−i−i000010-100
χ332222-2-2-12-2-2-12-12-12-121-2-1-1-11-211-2-21111112i−2i-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii0020-202i−2i00−i−iii0000000-101000
χ342222-2-2-12-2-2-12-12-12-121-2-1-1-11-211-2-21111112i−2i-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii00-2020−2i2i00ii−i−i000000010-1000
χ352222-2-2-12-2-2-12-12-12-121-2-1-1-11-211-2-2111111−2i2i-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i0020-20−2i2i00ii−i−i0000000-101000
χ362222-2-2-12-2-2-12-12-12-121-2-1-1-11-211-2-2111111−2i2i-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i00-20202i−2i00−i−iii000000010-1000
χ374444444-2-4-44-24-24-2-2-44-2-2-2-24-2-4-4222222-2-200-42220000000000000000000000000000000000000000000
χ38444444-24-4-4-24-24-24-2-4-24-2-2-2-2422-4-42222-2-2002-4220000000000000000000000000000000000000000000
χ39444444-2-244-2-2-2-2-2-214-2-2111-2-2-2-2-2-211111144-2-211-2-2-2-21111-2-2-2-21111000000000000000000000000000
χ40444444-2-244-2-2-2-2-2-214-2-2111-2-2-2-2-2-2111111-4-4-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000
χ41444444-2-2-4-4-2-2-2-2-2-21-4-2-2111-2-22222-1-1-1-1110022-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000
χ42444444-2-2-4-4-2-2-2-2-2-21-4-2-2111-2-22222-1-1-1-1110022-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000
χ434444-4-44-2444-24-24-2-2-4-42-2-2-2-4244-2-2-2-2-2-22200-42220000000000000000000000000000000000000000000
χ444444-4-4-2444-24-24-24-2-42-4-2-2-22-4-2-244-2-2-2-222002-4220000000000000000000000000000000000000000000
χ454444-4-4-2-244-2-2-2-2-2-21-42211122-2-2-2-21111-1-10022-1-1000033-3-30000-3-333000000000000000000000000000
χ464444-4-4-2-244-2-2-2-2-2-21-42211122-2-2-2-21111-1-10022-1-10000-3-333000033-3-3000000000000000000000000000
χ474444-4-4-2-2-4-4-2-2-2-2-2-21422111222222-1-1-1-1-1-14i−4i-2-211−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000
χ484444-4-4-2-2-4-4-2-2-2-2-2-21422111222222-1-1-1-1-1-1−4i4i-2-2112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000000
χ4944-4-4004400-4-444-4-44000-4-4400000000000000000000000000000000004i−4i0000000000000000000000000
χ5044-4-4004400-4-444-4-44000-4-440000000000000000000000000000000000−4i4i0000000000000000000000000
χ514-44-400444i−4i44-4-4-4-440004-4-4004i−4i4i−4i4i4i−4i−4i000000000000000000000000000000000000000000000000000
χ524-44-40044−4i4i44-4-4-4-440004-4-400−4i4i−4i4i−4i−4i4i4i000000000000000000000000000000000000000000000000000
χ534-44-4004-24i−4i4-2-42-42-2000-222004i−4i−2i2i−2i−2i2i2i00000000000000000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000
χ544-44-4004-24i−4i4-2-42-42-2000-222004i−4i−2i2i−2i−2i2i2i00000000000000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000
χ554-44-4004-2−4i4i4-2-42-42-2000-22200−4i4i2i−2i2i2i−2i−2i00000000000000000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000
χ564-44-4004-2−4i4i4-2-42-42-2000-22200−4i4i2i−2i2i2i−2i−2i00000000000000000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000
χ574-44-400-244i−4i-242-42-4-2000-22200−2i2i4i−4i−2i−2i2i2i0000000000000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000
χ584-44-400-244i−4i-242-42-4-2000-22200−2i2i4i−4i−2i−2i2i2i0000000000000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000
χ594-44-400-24−4i4i-242-42-4-2000-222002i−2i−4i4i2i2i−2i−2i0000000000000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000
χ604-44-400-24−4i4i-242-42-4-2000-222002i−2i−4i4i2i2i−2i−2i0000000000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000
χ614-4-444-44400-4-4-4-444404-4-44-4-44000000004-40000000000000000000000000000000000000000000000000
χ624-4-444-44-200-42-424-2-20422-22-4-200000000-2200000000i6−i6i6−i6i6−i600i6−i6i6−i6i6−i6000000000000000000000000000
χ634-4-444-44-200-42-424-2-20422-22-4-200000000-2200000000−i6i6−i6i6−i6i600−i6i6−i6i6−i6i6000000000000000000000000000
χ644-4-444-4-24002-42-4-24-20-2-42-222400000000-220000006−6006−6−666−6006−6−66000000000000000000000000000
χ654-4-444-4-24002-42-4-24-20-2-42-222400000000-22000000−6600−666−6−6600−666−6000000000000000000000000000
χ664-4-444-4-2-2002222-2-210-22-11-12-200003i−3i3i−3i1-100003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ674-4-444-4-2-2002222-2-210-22-11-12-200003i−3i3i−3i1-100003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ684-4-444-4-2-2002222-2-210-22-11-12-20000−3i3i−3i3i1-10000−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ694-4-444-4-2-2002222-2-210-22-11-12-20000−3i3i−3i3i1-10000−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ704-4-44-444400-4-4-4-44440-44-44-44-400000000-440000000000000000000000000000000000000000000000000
χ714-4-44-444-200-42-424-2-20-4-22-2242000000002-2000000006−66−66−600−66−66−66000000000000000000000000000
χ724-4-44-444-200-42-424-2-20-4-22-2242000000002-200000000−66−66−66006−66−66−6000000000000000000000000000
χ734-4-44-44-24002-42-4-24-20242-22-2-4000000002-2000000i6−i600i6−i6−i6i6−i6i600−i6i6i6−i6000000000000000000000000000
χ744-4-44-44-24002-42-4-24-20242-22-2-4000000002-2000000−i6i600−i6i6i6−i6i6−i600i6−i6−i6i6000000000000000000000000000
χ754-4-44-44-2-2002222-2-2102-2-11-1-2200003i−3i3i−3i-110000−3i3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ764-4-44-44-2-2002222-2-2102-2-11-1-2200003i−3i3i−3i-110000−3i3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ774-4-44-44-2-2002222-2-2102-2-11-1-220000−3i3i−3i3i-1100003i−3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ784-4-44-44-2-2002222-2-2102-2-11-1-220000−3i3i−3i3i-1100003i−3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ7988-8-8008-400-848-4-84-400044-40000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-48004-8-484-8-400044-40000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-4-40044-4-4442000-2-220000006-6-66000000000000000000000000000000000000000000000000000
χ8288-8-800-4-40044-4-4442000-2-22000000-666-6000000000000000000000000000000000000000000000000000
χ838-88-800-4-48i−8i-4-4444420002-2-200−4i4i−4i4i2i2i−2i−2i000000000000000000000000000000000000000000000000000
χ848-88-800-4-4−8i8i-4-4444420002-2-2004i−4i4i−4i−2i−2i2i2i000000000000000000000000000000000000000000000000000

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