Finite Group Databasebeta

← Group #11771211

Character table — Group #11771211

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222444444444444444448888888899991212121212121212121212121212121218181818242424242424242424242424242424243672727272
order12222244334666666666612121212661212121212124444444444448888888844441212121212121212242424242424242448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−i1ii−i−i
χ6111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−i−i−iiiii1−i−iii
χ7111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-1-1-11111iiii−i−i−i−i1−i−iii
χ8111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-1-1-11111−i−i−i−iiiii1ii−i−i
χ91111-1-11111-11111-1-1-111-11111-1-111-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-111-1-1-1-111ii−i−iii−i−i11-1-111-1-11i−ii−i
χ101111-1-11111-11111-1-1-111-11111-1-111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-111-1-111-1-111ii−i−iii−i−i-1-111-1-1111−ii−ii
χ111111-1-11111-11111-1-1-111-11111-1-111-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-111-1-1-1-111−i−iii−i−iii11-1-111-1-11−ii−ii
χ121111-1-11111-11111-1-1-111-11111-1-111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-111-1-111-1-111−i−iii−i−iii-1-111-1-1111i−ii−i
χ131111-1-1-1-11111111-1-1-111-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii1-111-1
χ141111-1-1-1-11111111-1-1-111-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-11
χ151111-1-1-1-11111111-1-1-111-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii-1-1-1-1−i−iiiii−i−iii−i−i−i−iii11-1-11
χ161111-1-1-1-11111111-1-1-111-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i1-111-1
χ17222222222222222222222222222222222-2-2-2-20000000000000000-2-2-2-20000000000000000-20000
χ18222222-2-222-22222222222-2-2-2-222-2-2-2-2-2-222220000000000000000-2-2220000000000000000-20000
χ192222-2-22222-22222-2-2-222-22222-2-222-2-2-2-22222000000000000000022-2-20000000000000000-20000
χ202222-2-2-2-22222222-2-2-222-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000022220000000000000000-20000
χ2122-2-2002-2220-2-2-2-200022022-2-2002-200002i−2i2i−2i1+i−1−i1−i−1+i1+i−1−i1−i−1+i000000002i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000000000
χ2222-2-2002-2220-2-2-2-200022022-2-2002-200002i−2i2i−2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000002i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000000
χ2322-2-2002-2220-2-2-2-200022022-2-2002-20000−2i2i−2i2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000000000000
χ2422-2-2002-2220-2-2-2-200022022-2-2002-20000−2i2i−2i2i−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000000000000
χ2522-2-200-22220-2-2-2-2000220-2-22200-2200002i−2i2i−2i1−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000−2i2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000000000000
χ2622-2-200-22220-2-2-2-2000220-2-22200-2200002i−2i2i−2i−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000−2i2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000000000000
χ2722-2-200-22220-2-2-2-2000220-2-22200-220000−2i2i−2i2i1+i−1−i1−i−1+i−1−i1+i−1+i1−i000000002i−2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000000000000
χ2822-2-200-22220-2-2-2-2000220-2-22200-220000−2i2i−2i2i−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000002i−2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000000000000
χ292-22-22-20022022-2-222-2-2-2-200002-200000022-2-2000000002−22−22−22−2002-2000000002−22−22−22−200000
χ302-22-22-20022022-2-222-2-2-2-200002-200000022-2-200000000−22−22−22−22002-200000000−22−22−22−2200000
χ312-22-22-20022022-2-222-2-2-2-200002-2000000-2-22200000000i2−i2i2−i2−i2i2−i2i200-2200000000i2−i2i2−i2−i2i2−i2i200000
χ322-22-22-20022022-2-222-2-2-2-200002-2000000-2-22200000000−i2i2−i2i2i2−i2i2−i200-2200000000−i2i2−i2i2i2−i2i2−i200000
χ332-22-2-220022022-2-2-2-22-2-220000-2200000022-2-200000000i2−i2−i2i2−i2i2i2−i200-2200000000i2−i2−i2i2−i2i2i2−i200000
χ342-22-2-220022022-2-2-2-22-2-220000-2200000022-2-200000000−i2i2i2−i2i2−i2−i2i200-2200000000−i2i2i2−i2i2−i2−i2i200000
χ352-22-2-220022022-2-2-2-22-2-220000-22000000-2-222000000002−2−222−2−22002-2000000002−2−222−2−2200000
χ362-22-2-220022022-2-2-2-22-2-220000-22000000-2-22200000000−222−2−222−2002-200000000−222−2−222−200000
χ37444444441-241-21-21111-21-2-2-2-2-2-21111-2-2000022222222000000000000-1-1-1-1-1-1-1-10000000000000
χ38444444441-241-21-21111-21-2-2-2-2-2-21111-2-20000-2-2-2-2-2-2-2-2000000000000111111110000000000000
χ3944444444-214-21-21-2-2-2-21-2111111-2-2-2-21100000000000022222222000000000000-1-1-1-1-1-1-1-100000
χ4044444444-214-21-21-2-2-2-21-2111111-2-2-2-211000000000000-2-2-2-2-2-2-2-20000000000001111111100000
χ41444444-4-41-2-41-21-21111-212222-2-2-1-1-1-12200002222-2-2-2-2000000000000-1-1-1-111110000000000000
χ42444444-4-41-2-41-21-21111-212222-2-2-1-1-1-1220000-2-2-2-222220000000000001111-1-1-1-10000000000000
χ43444444-4-4-21-4-21-21-2-2-2-21-2-1-1-1-1112222-1-10000000000002i2i2i2i−2i−2i−2i−2i000000000000−i−i−i−iiiii00000
χ44444444-4-4-21-4-21-21-2-2-2-21-2-1-1-1-1112222-1-1000000000000−2i−2i−2i−2i2i2i2i2i000000000000iiii−i−i−i−i00000
χ454444-4-4441-2-41-21-2-1-1-11-2-1-2-2-2-22211-1-12200002i2i−2i−2i2i2i−2i−2i000000000000−i−iii−i−iii0000000000000
χ464444-4-4441-2-41-21-2-1-1-11-2-1-2-2-2-22211-1-1220000−2i−2i2i2i−2i−2i2i2i000000000000ii−i−iii−i−i0000000000000
χ474444-4-444-21-4-21-21222-2121111-1-1-2-222-1-100000000000022-2-222-2-2000000000000-1-111-1-11100000
χ484444-4-444-21-4-21-21222-2121111-1-1-2-222-1-1000000000000-2-222-2-22200000000000011-1-111-1-100000
χ494444-4-4-4-41-241-21-2-1-1-11-2-1222222-1-111-2-200002i2i−2i−2i−2i−2i2i2i000000000000−i−iiiii−i−i0000000000000
χ504444-4-4-4-41-241-21-2-1-1-11-2-1222222-1-111-2-20000−2i−2i2i2i2i2i−2i−2i000000000000ii−i−i−i−iii0000000000000
χ514444-4-4-4-4-214-21-21222-212-1-1-1-1-1-122-2-2110000000000002i2i−2i−2i−2i−2i2i2i000000000000−i−iiiii−i−i00000
χ524444-4-4-4-4-214-21-21222-212-1-1-1-1-1-122-2-211000000000000−2i−2i2i2i2i2i−2i−2i000000000000ii−i−i−i−iii00000
χ5344-4-4004-41-20-12-123-331-2-3-2-222001-13-30000002-22-22-22-2000000000000-11-11-11-110000000000000
χ5444-4-4004-41-20-12-123-331-2-3-2-222001-13-3000000-22-22-22-220000000000001-11-11-11-10000000000000
χ5544-4-4004-41-20-12-12-33-31-23-2-222001-1-330000002i−2i−2i2i2i−2i−2i2i000000000000−iii−i−iii−i0000000000000
χ5644-4-4004-41-20-12-12-33-31-23-2-222001-1-33000000−2i2i2i−2i−2i2i2i−2i000000000000i−i−iii−i−ii0000000000000
χ5744-4-400-441-20-12-123-331-2-322-2-200-11-330000002-22-2-22-22000000000000-11-111-11-10000000000000
χ5844-4-400-441-20-12-123-331-2-322-2-200-11-33000000-22-222-22-20000000000001-11-1-11-110000000000000
χ5944-4-400-441-20-12-12-33-31-2322-2-200-113-30000002i−2i−2i2i−2i2i2i−2i000000000000−iii−ii−i−ii0000000000000
χ6044-4-400-441-20-12-12-33-31-2322-2-200-113-3000000−2i2i2i−2i2i−2i−2i2i000000000000i−i−ii−iii−i0000000000000
χ614-44-44-400-210-212-1-2-222-123i−3i3i−3i1-100003i−3i0000000000002ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3000000000000−ζζ−ζζζ3−ζ3ζ3−ζ300000
χ624-44-44-400-210-212-1-2-222-123i−3i3i−3i1-100003i−3i000000000000−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ3000000000000ζ−ζζ−ζ−ζ3ζ3−ζ3ζ300000
χ634-44-44-400-210-212-1-2-222-12−3i3i−3i3i1-10000−3i3i0000000000002ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ000000000000−ζ3ζ3−ζ3ζ3ζ−ζζ−ζ00000
χ644-44-44-400-210-212-1-2-222-12−3i3i−3i3i1-10000−3i3i000000000000−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ000000000000ζ3−ζ3ζ3−ζ3−ζζ−ζζ00000
χ654-44-4-4400-210-212-122-22-1-23i−3i3i−3i-110000−3i3i0000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000−ζζζ−ζζ3−ζ3−ζ3ζ300000
χ664-44-4-4400-210-212-122-22-1-23i−3i3i−3i-110000−3i3i000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000ζ−ζ−ζζ−ζ3ζ3ζ3−ζ300000
χ674-44-4-4400-210-212-122-22-1-2−3i3i−3i3i-1100003i−3i0000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000−ζ3ζ3ζ3−ζ3ζ−ζ−ζζ00000
χ684-44-4-4400-210-212-122-22-1-2−3i3i−3i3i-1100003i−3i000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000ζ3−ζ3−ζ3ζ3−ζζζ−ζ00000
χ694-4-440000440-4-444000-4-400000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ704-4-440000440-4-444000-4-40000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ7188-8-8008-8-4204-24-2000-42022-2-200-440000000000000000000000000000000000000000000000000
χ7288-8-800-88-4204-24-2000-420-2-222004-40000000000000000000000000000000000000000000000000
χ738-88-88-8002-402-4-2422-2-24-20000-44000000000000000000000000000000000000000000000000000
χ748-88-8-88002-402-4-24-2-22-24200004-4000000000000000000000000000000000000000000000000000
χ758-8-8800002-40-242-46-6-6-246000000000000000000000000000000000000000000000000000000000
χ768-8-8800002-40-242-4-666-24-6000000000000000000000000000000000000000000000000000000000
χ778-8-880000-4204-2-420004-206i−6i−6i6i00000000000000000000000000000000000000000000000000000
χ788-8-880000-4204-2-420004-20−6i6i6i−6i00000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.