Finite Group Databasebeta

← Group #11775128

Character table — Group #11775128

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222244444444444444444888888888888888888888888121212121212121218181818181824242424242424242424242436484848487272
order122222334466666634666666612121212121212126688121212122424242424242424242424242424242444444444222244244412121212121212124612121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111
χ511111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111111-1-1-1-1-1-1
χ611111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-111-1-111
χ811111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1
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−iii−i−iii−i−i11-1-1111-1-11ii−i−iii−i−i-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−iii−i−i−i−iii-1-111-1-11-11-1ii−i−i−i−iii11-11-1−ii
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−i−iiiii−i−i-1-111-1-1-11-11−i−iiiii−i−i1-11-11−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−i−iii−i−iii11-1-111-111-1−i−iii−i−iii-1-111-1i−i
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−iiiiiiiiiii−i−iii−i−i11-1-111-111-1ii−i−iii−i−i-1-111-1−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−iiiiiiiiiii−i−i−i−iii-1-111-1-1-11-11ii−i−i−i−iii1-11-11i−i
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−i−iiiii−i−i-1-111-1-11-11-1−i−iiiii−i−i11-11-1i−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−i−iii−i−iii11-1-1111-1-11−i−iii−i−iii-11-1-11−ii
χ1722222222-2-22222222-22222222-2-2-2-2-2-2-2-22200-2-2-2-20000000000000000000000002222-2-2000000000000-2000000
χ1822222222-2-22222222-22222222-2-2-2-2-2-2-2-22200-2-2-2-2000000000000000000000000-2-2-2-2220000000000002000000
χ192222222-1222-1-12-12-122-1-1-1-12-1-1-122-1-1-1-1-1-122-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1222200000000002200-1-1-1-100000-1-10000
χ202222222-1222-1-12-12-122-1-1-1-12-1-1-122-1-1-1-1-1-122-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-20000000000-2-200111100000110000
χ212222222-1222-1-12-12-122-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-12-1-1-2-2111111-2-211111122220000000000-2-200-1-1-1-100000110000
χ222222222-1222-1-12-12-122-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-12-1-1-2-2111111-2-2111111-2-2-2-200000000002200111100000-1-10000
χ23222222-1222-122-12-1-12-12-1-1-1-1222-1-1-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000222200000000220000-1-1-1-1000-1-100
χ24222222-1222-122-12-1-12-12-1-1-1-1222-1-1-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-2-2-200000000-2-2000011110001100
χ25222222-1222-122-12-1-12-12-1-1-1-1222-1-1-1-1-1-1-1-1-2-22-1-1-111-2-2111111-2-211110000222200000000-2-20000-1-1-1-10001100
χ26222222-1222-122-12-1-12-12-1-1-1-1222-1-1-1-1-1-1-1-1-2-22-1-1-111-2-2111111-2-211110000-2-2-2-2000000002200001111000-1-100
χ272222-2-222222222222-2-2-2222-2-222222222-2-200-2-2-2-200000000000000000000000022-2-2-2-20000000000002000000
χ282222-2-222222222222-2-2-2222-2-222222222-2-200-2-2-2-2000000000000000000000000-2-22222000000000000-2000000
χ292222-2-22-1-2-22-1-12-12-12-21-1-1-1-2111-2-21111112i−2i-12-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii2i2i−2i−2i00000000002-200−i−iii00000-110000
χ302222-2-22-1-2-22-1-12-12-12-21-1-1-1-2111-2-21111112i−2i-12-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii−2i−2i2i2i0000000000-2200ii−i−i000001-10000
χ312222-2-22-1-2-22-1-12-12-12-21-1-1-1-2111-2-2111111−2i2i-12-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i2i2i−2i−2i0000000000-2200−i−iii000001-10000
χ322222-2-22-1-2-22-1-12-12-12-21-1-1-1-2111-2-2111111−2i2i-12-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i−2i−2i2i2i00000000002-200ii−i−i00000-110000
χ332222-2-2-12-2-2-122-12-1-121-2-1-1-11-2-2-2111111112i−2i2-1-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii00002i2i−2i−2i00000000-220000−i−iii0001-100
χ342222-2-2-12-2-2-122-12-1-121-2-1-1-11-2-2-2111111112i−2i2-1-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii0000−2i−2i2i2i000000002-20000ii−i−i000-1100
χ352222-2-2-12-2-2-122-12-1-121-2-1-1-11-2-2-211111111−2i2i2-1-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i00002i2i−2i−2i000000002-20000−i−iii000-1100
χ362222-2-2-12-2-2-122-12-1-121-2-1-1-11-2-2-211111111−2i2i2-1-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i0000−2i−2i2i2i00000000-220000ii−i−i0001-100
χ3722-2-200222i−2i-22-22-2-220002-2-2002i−2i2i−2i2i2i−2i−2i0000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i002-22i−2i00001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000
χ3822-2-200222i−2i-22-22-2-220002-2-2002i−2i2i−2i2i2i−2i−2i0000000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00-22−2i2i00001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000
χ3922-2-200222i−2i-22-22-2-220002-2-2002i−2i2i−2i2i2i−2i−2i000000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00-22−2i2i0000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000
χ4022-2-200222i−2i-22-22-2-220002-2-2002i−2i2i−2i2i2i−2i−2i000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i002-22i−2i0000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000
χ4122-2-20022−2i2i-22-22-2-220002-2-200−2i2i−2i2i−2i−2i2i2i0000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i002-2−2i2i00001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000
χ4222-2-20022−2i2i-22-22-2-220002-2-200−2i2i−2i2i−2i−2i2i2i0000000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00-222i−2i00001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000
χ4322-2-20022−2i2i-22-22-2-220002-2-200−2i2i−2i2i−2i−2i2i2i000000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00-222i−2i0000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000
χ4422-2-20022−2i2i-22-22-2-220002-2-200−2i2i−2i2i−2i−2i2i2i000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i002-2−2i2i0000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000
χ454444444-2-4-44-2-24-24-2-44-2-2-2-24-222-4-42222-2-2002-4220000000000000000000000000000000000000000000000000
χ46444444-24-4-4-244-24-2-2-4-24-2-2-2-24-4-4222222-2-200-42220000000000000000000000000000000000000000000000000
χ47444444-2-244-2-2-2-2-2-214-2-2111-2-2-2-2-2-211111144-2-211-2-2-2-21111-2-2-2-21111000000000000000000000000000000000
χ48444444-2-244-2-2-2-2-2-214-2-2111-2-2-2-2-2-2111111-4-4-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000
χ49444444-2-2-4-4-2-2-2-2-2-21-4-2-2111-2-22222-1-1-1-1110022-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000000
χ50444444-2-2-4-4-2-2-2-2-2-21-4-2-2111-2-22222-1-1-1-1110022-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000000
χ514444-4-44-2444-2-24-24-2-4-42-2-2-2-42-2-244-2-2-2-222002-4220000000000000000000000000000000000000000000000000
χ524444-4-4-2444-244-24-2-2-42-4-2-2-22-444-2-2-2-2-2-22200-42220000000000000000000000000000000000000000000000000
χ534444-4-4-2-244-2-2-2-2-2-21-42211122-2-2-2-21111-1-10022-1-1000033-3-30000-3-333000000000000000000000000000000000
χ544444-4-4-2-244-2-2-2-2-2-21-42211122-2-2-2-21111-1-10022-1-10000-3-333000033-3-3000000000000000000000000000000000
χ554444-4-4-2-2-4-4-2-2-2-2-2-21422111222222-1-1-1-1-1-14i−4i-2-211−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000000000
χ564444-4-4-2-2-4-4-2-2-2-2-2-21422111222222-1-1-1-1-1-1−4i4i-2-2112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000000000000
χ5744-4-4004-24i−4i-4-2242-4-2000-22200−2i2i4i−4i−2i−2i2i2i0000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000−1−i1+i−1+i1−i00000000000
χ5844-4-4004-24i−4i-4-2242-4-2000-22200−2i2i4i−4i−2i−2i2i2i000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000001+i−1−i1−i−1+i00000000000
χ5944-4-4004-2−4i4i-4-2242-4-2000-222002i−2i−4i4i2i2i−2i−2i0000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000−1+i1−i−1−i1+i00000000000
χ6044-4-4004-2−4i4i-4-2242-4-2000-222002i−2i−4i4i2i2i−2i−2i000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000001−i−1+i1+i−1−i00000000000
χ6144-4-400-244i−4i24-4-2-42-2000-222004i−4i−2i2i−2i−2i2i2i00000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000−1+i1−i−1−i1+i0000000
χ6244-4-400-244i−4i24-4-2-42-2000-222004i−4i−2i2i−2i−2i2i2i0000000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000001−i−1+i1+i−1−i0000000
χ6344-4-400-24−4i4i24-4-2-42-2000-22200−4i4i2i−2i2i2i−2i−2i00000000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000−1−i1+i−1+i1−i0000000
χ6444-4-400-24−4i4i24-4-2-42-2000-22200−4i4i2i−2i2i2i−2i−2i0000000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000001+i−1−i1−i−1+i0000000
χ654-44-44-444004-4-4-44-44044-44-4-4-4000000004-40000000000000000000000000000000000000000000000000000000
χ664-44-44-44-200422-4-2-4-204-22-22-4200000000-22000000006−66−66−6006−66−66−6000000000000000000000000000000000
χ674-44-44-44-200422-4-2-4-204-22-22-4200000000-2200000000−66−66−6600−66−66−66000000000000000000000000000000000
χ684-44-44-4-2400-2-4-4242-20-242-222-400000000-22000000i6−i600i6−i6−i6i6i6−i600i6−i6−i6i6000000000000000000000000000000000
χ694-44-44-4-2400-2-4-4242-20-242-222-400000000-22000000−i6i600−i6i6i6−i6−i6i600−i6i6i6−i6000000000000000000000000000000000
χ704-44-44-4-2-200-2222-2210-2-2-11-12200003i−3i3i−3i1-100003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ714-44-44-4-2-200-2222-2210-2-2-11-12200003i−3i3i−3i1-100003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ724-44-44-4-2-200-2222-2210-2-2-11-1220000−3i3i−3i3i1-10000−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ734-44-44-4-2-200-2222-2210-2-2-11-1220000−3i3i−3i3i1-10000−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ744-44-4-4444004-4-4-44-440-4-4-44-44400000000-440000000000000000000000000000000000000000000000000000000
χ754-44-4-444-200422-4-2-4-20-422-224-2000000002-200000000i6−i6i6−i6i6−i600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ764-44-4-444-200422-4-2-4-20-422-224-2000000002-200000000−i6i6−i6i6−i6i600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ774-44-4-44-2400-2-4-4242-202-42-22-24000000002-20000006−6006−6−66−6600−666−6000000000000000000000000000000000
χ784-44-4-44-2400-2-4-4242-202-42-22-24000000002-2000000−6600−666−66−6006−6−66000000000000000000000000000000000
χ794-44-4-44-2-200-2222-221022-11-1-2-200003i−3i3i−3i-110000−3i3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ804-44-4-44-2-200-2222-221022-11-1-2-200003i−3i3i−3i-110000−3i3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ814-44-4-44-2-200-2222-221022-11-1-2-20000−3i3i−3i3i-1100003i−3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ824-44-4-44-2-200-2222-221022-11-1-2-20000−3i3i−3i3i-1100003i−3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ834-4-44004400-4-44-4-444000-4-440000000000000000000000000000000000000000004-400000000000000000000000
χ844-4-44004400-4-44-4-444000-4-44000000000000000000000000000000000000000000-4400000000000000000000000
χ8588-8-800-4-48i−8i4-44-44420002-2-200−4i4i−4i4i2i2i−2i−2i000000000000000000000000000000000000000000000000000000000
χ8688-8-800-4-4−8i8i4-44-44420002-2-2004i−4i4i−4i−2i−2i2i2i000000000000000000000000000000000000000000000000000000000
χ878-8-88008-400-84-4-848-400044-40000000000000000000000000000000000000000000000000000000000000000000
χ888-8-8800-48004-884-8-4-400044-40000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800-4-40044-444-42000-2-220000006-6-66000000000000000000000000000000000000000000000000000000000
χ908-8-8800-4-40044-444-42000-2-22000000-666-6000000000000000000000000000000000000000000000000000000000

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