Finite Group Databasebeta

← Group #11774482

Character table — Group #11774482

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222244444444444448888888888999912121212121212121818181824242424242424242424242436363636363636363648484848
order122222443346666661212121266661212121212124444888888884444244424242424242424244888888886121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ5111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i1iiii−i−i−i−i1-1-11
χ6111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1-1-111iiii−i−i−i−i1−i−i−i−iiiii-111-1
χ7111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii1−i−i−i−iiiii1-1-11
χ8111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1-1-111−i−i−i−iiiii1iiii−i−i−i−i-111-1
χ91111-1-11111-11111111111-1-1-1-1-1-111-1-1111111-1-111-1-111-1-11-11-111-1-111-1-1-111-1-111-1-111-1-1
χ101111-1-11111-11111111111-1-1-1-1-1-111-1-1111111-1-111-1-111-1-1-11-1111-1-111-1-1-1-1-111-1-111-1-111
χ111111-1-11111-11111111111-1-1-1-1-1-111-1-11111-1-111-1-11111-1-11-11-1-1-111-1-111-1-1-111-1-11111-1-1
χ121111-1-11111-11111111111-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1-11-11-1-111-1-111-111-1-111-1-1-1-111
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i−i−iii11111-1-11ii−i−i−i−iii-1ii−i−i−i−iii1-11-1
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i−i−iii1111-111-1ii−i−i−i−iii-1−i−iiiii−i−i-11-11
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1−i−iiiii−i−i11111-1-11−i−iiiii−i−i-1−i−iiiii−i−i1-11-1
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1−i−iiiii−i−i1111-111-1−i−iiiii−i−i-1ii−i−i−i−iii-11-11
χ172222222222222222222222222222222-2-2-2-200000000-2-2-2-2000000000000-2000000000000
χ18222222-2-222-2222222-2-2-2-22222-2-2-2-2-2-2222200000000-2-222000000000000-2000000000000
χ192222-2-22222-22222222222-2-2-2-2-2-222-2-2-2-2-2-200000000-2-2220000000000002000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-222222200000000-2-2-2-20000000000002000000000000
χ2122-2-22-200220-2-22-2-2200002-22-20000002i−2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000
χ2222-2-22-200220-2-22-2-2200002-22-20000002i−2i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000
χ2322-2-22-200220-2-22-2-2200002-22-2000000−2i2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000
χ2422-2-22-200220-2-22-2-2200002-22-2000000−2i2i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000
χ2522-2-2-2200220-2-22-2-220000-22-220000002i−2i2i−2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00−2i2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000
χ2622-2-2-2200220-2-22-2-220000-22-220000002i−2i2i−2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00−2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000
χ2722-2-2-2200220-2-22-2-220000-22-22000000−2i2i−2i2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i002i−2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000
χ2822-2-2-2200220-2-22-2-220000-22-22000000−2i2i−2i2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i002i−2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000
χ292-22-2002i−2i2202-2-22-2-22i−2i2i−2i0000002i−2i002i−2i−2i2i000000002-2000000000000000002ζ3−2ζ3002ζ−2ζ0000
χ302-22-2002i−2i2202-2-22-2-22i−2i2i−2i0000002i−2i002i−2i−2i2i000000002-200000000000000000−2ζ32ζ300−2ζ2ζ0000
χ312-22-2002i−2i2202-2-22-2-22i−2i2i−2i0000002i−2i00−2i2i2i−2i00000000-220000000000000002ζ−2ζ002ζ3−2ζ3000000
χ322-22-2002i−2i2202-2-22-2-22i−2i2i−2i0000002i−2i00−2i2i2i−2i00000000-22000000000000000−2ζ2ζ00−2ζ32ζ3000000
χ332-22-200−2i2i2202-2-22-2-2−2i2i−2i2i000000−2i2i002i−2i−2i2i00000000-220000000000000002ζ3−2ζ3002ζ−2ζ000000
χ342-22-200−2i2i2202-2-22-2-2−2i2i−2i2i000000−2i2i002i−2i−2i2i00000000-22000000000000000−2ζ32ζ300−2ζ2ζ000000
χ352-22-200−2i2i2202-2-22-2-2−2i2i−2i2i000000−2i2i00−2i2i2i−2i000000002-2000000000000000002ζ−2ζ002ζ3−2ζ30000
χ362-22-200−2i2i2202-2-22-2-2−2i2i−2i2i000000−2i2i00−2i2i2i−2i000000002-200000000000000000−2ζ2ζ00−2ζ32ζ30000
χ37444444441-24111-2-2-2111111-2-211-2-2-2-200002222222200000000-1-1-1-1-1-1-1-10000000000000
χ38444444441-24111-2-2-2111111-2-211-2-2-2-20000-2-2-2-2-2-2-2-200000000111111110000000000000
χ3944444444-214-2-2-2111-2-2-2-2-2-211-2-211110000000000000000222200000000000000000-1-1-1-1
χ4044444444-214-2-2-2111-2-2-2-2-2-211-2-211110000000000000000-2-2-2-2000000000000000001111
χ41444444-4-41-2-4111-2-2-2-1-1-1-111-2-2-1-1222200002i2i2i2i−2i−2i−2i−2i00000000−i−i−i−iiiii0000000000000
χ42444444-4-41-2-4111-2-2-2-1-1-1-111-2-2-1-122220000−2i−2i−2i−2i2i2i2i2i00000000iiii−i−i−i−i0000000000000
χ43444444-4-4-21-4-2-2-21112222-2-21122-1-1-1-1000000000000000022-2-200000000000000000-111-1
χ44444444-4-4-21-4-2-2-21112222-2-21122-1-1-1-10000000000000000-2-222000000000000000001-1-11
χ454444-4-4441-2-4111-2-2-21111-1-122-1-1-2-222000022-2-222-2-200000000-1-111-1-1110000000000000
χ464444-4-4441-2-4111-2-2-21111-1-122-1-1-2-2220000-2-222-2-2220000000011-1-111-1-10000000000000
χ474444-4-444-21-4-2-2-2111-2-2-2-222-1-12211-1-100000000000000002-22-200000000000000000-1-111
χ484444-4-444-21-4-2-2-2111-2-2-2-222-1-12211-1-10000000000000000-22-220000000000000000011-1-1
χ494444-4-4-4-41-24111-2-2-2-1-1-1-1-1-1221122-2-200002i2i−2i−2i−2i−2i2i2i00000000−i−iiiii−i−i0000000000000
χ504444-4-4-4-41-24111-2-2-2-1-1-1-1-1-1221122-2-20000−2i−2i2i2i2i2i−2i−2i00000000ii−i−i−i−iii0000000000000
χ514444-4-4-4-4-214-2-2-2111222222-1-1-2-2-1-11100000000000000002-2-2200000000000000000-11-11
χ524444-4-4-4-4-214-2-2-2111222222-1-1-2-2-1-1110000000000000000-222-2000000000000000001-11-1
χ5344-4-44-4001-20-1-1122-233-3-31-1-223-3000000002-22-22-22-200000000-11-11-11-110000000000000
χ5444-4-44-4001-20-1-1122-233-3-31-1-223-300000000-22-22-22-22000000001-11-11-11-10000000000000
χ5544-4-44-4001-20-1-1122-2-3-3331-1-22-33000000002i−2i2i−2i−2i2i−2i2i00000000−ii−iii−ii−i0000000000000
χ5644-4-44-4001-20-1-1122-2-3-3331-1-22-3300000000−2i2i−2i2i2i−2i2i−2i00000000i−ii−i−ii−ii0000000000000
χ5744-4-4-44001-20-1-1122-233-3-3-112-2-33000000002-2-222-2-2200000000-111-1-111-10000000000000
χ5844-4-4-44001-20-1-1122-233-3-3-112-2-3300000000-222-2-222-2000000001-1-111-1-110000000000000
χ5944-4-4-44001-20-1-1122-2-3-333-112-23-3000000002i−2i−2i2i−2i2i2i−2i00000000−iii−ii−i−ii0000000000000
χ6044-4-4-44001-20-1-1122-2-3-333-112-23-300000000−2i2i2i−2i2i−2i−2i2i00000000i−i−ii−iii−i0000000000000
χ614-4-440000440-44-4-44-40000000000000044-4-40000000000000000000000000000000000000
χ624-4-440000440-44-4-44-400000000000000-4-4440000000000000000000000000000000000000
χ6388-8-88-800-42044-4-2-220000-442-200000000000000000000000000000000000000000000000
χ6488-8-8-8800-42044-4-2-2200004-4-2200000000000000000000000000000000000000000000000
χ658-88-8008i−8i2-402-2-2-4442i−2i2i−2i000000−4i4i0000000000000000000000000000000000000000000
χ668-88-8008i−8i-420-4442-2-2−4i4i−4i4i0000002i−2i0000000000000000000000000000000000000000000
χ678-88-800−8i8i2-402-2-2-444−2i2i−2i2i0000004i−4i0000000000000000000000000000000000000000000
χ688-88-800−8i8i-420-4442-2-24i−4i4i−4i000000−2i2i0000000000000000000000000000000000000000000
χ698-8-8800002-40-22-24-446i−6i−6i6i000000000000000000000000000000000000000000000000000
χ708-8-8800002-40-22-24-44−6i6i6i−6i000000000000000000000000000000000000000000000000000
χ718-8-880000-4204-44-22-20000000000006i−6i00000000000000000000000000000000000000000
χ728-8-880000-4204-44-22-2000000000000−6i6i00000000000000000000000000000000000000000

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