Finite Group Databasebeta

← Group #11791197

Character table — Group #11791197

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222224444444488888888888899991818181818181818181818181818181818181818181824242424242424244848484848484848
order12442444443366121212126612121212121212121212224424444488888888888888882244888866121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-11-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11-11-1-111
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-11-1-1-1111-11-1-1-111
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1111-1-1-11-1111-1-1
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911-1-1-11ii−i−i1111-1-1-1-1-1-111iiii−i−i−i−i11-1-1-1ii−i−i1iiii−i−i−i−i1111-1-1-1-111-1-1i−ii−i11-1-1i−ii−i
χ1011-1-1-11ii−i−i1111-1-1-1-1-1-111iiii−i−i−i−i11-1-1-1ii−i−i1iiii−i−i−i−i1111-1-1-1-1-1-111−ii−ii-1-111−ii−ii
χ1111-1-1-11ii−i−i1111-1-1-1-1-1-111iiii−i−i−i−i11-1-1-1ii−i−i1−i−i−i−iiiii-1-1-1-111111-1-11i−i−ii1-1-11i−i−ii
χ1211-1-1-11ii−i−i1111-1-1-1-1-1-111iiii−i−i−i−i11-1-1-1ii−i−i1−i−i−i−iiiii-1-1-1-11111-111-1−iii−i-111-1−iii−i
χ1311-1-1-11−i−iii1111-1-1-1-1-1-111−i−i−i−iiiii11-1-1-1−i−iii1iiii−i−i−i−i-1-1-1-111111-1-11−iii−i1-1-11−iii−i
χ1411-1-1-11−i−iii1111-1-1-1-1-1-111−i−i−i−iiiii11-1-1-1−i−iii1iiii−i−i−i−i-1-1-1-11111-111-1i−i−ii-111-1i−i−ii
χ1511-1-1-11−i−iii1111-1-1-1-1-1-111−i−i−i−iiiii11-1-1-1−i−iii1−i−i−i−iiiii1111-1-1-1-111-1-1−ii−ii11-1-1−ii−ii
χ1611-1-1-11−i−iii1111-1-1-1-1-1-111−i−i−i−iiiii11-1-1-1−i−iii1−i−i−i−iiiii1111-1-1-1-1-1-111i−ii−i-1-111i−ii−i
χ17222222222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22222-200000000000000000000000000000000
χ192222-2-2000022222222-2-2-2-2000000002222-20000-222-2-222-2-2000000000000000000000000
χ202222-2-2000022222222-2-2-2-2000000002222-20000-2-2-222-2-222000000000000000000000000
χ212222-2-2000022222222-2-2-2-200000000-2-2-2-22000020000000022-2-222-2-20000000000000000
χ222222-2-2000022222222-2-2-2-200000000-2-2-2-220000200000000-2-222-2-2220000000000000000
χ2322-2-22-200002222-2-2-2-222-2-20000000022-2-220000-22i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2422-2-22-200002222-2-2-2-222-2-20000000022-2-220000-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2522-2-22-200002222-2-2-2-222-2-200000000-2-222-2000020000000022-2-2-2-2220000000000000000
χ2622-2-22-200002222-2-2-2-222-2-200000000-2-222-20000200000000-2-22222-2-20000000000000000
χ2722-2-2-222i2i−2i−2i2222-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2-2222−2i−2i2i2i-200000000000000000000000000000000
χ2822-2-2-22−2i−2i2i2i2222-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2-22222i2i−2i−2i-200000000000000000000000000000000
χ292-22i−2i001+i−1−i1−i−1+i22-2-22i2i−2i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i01+i−1−i1−i−1+i0002ζ−2ζ002ζ3−2ζ32−22−2i2−i2i2−i20000000000000000
χ302-22i−2i001+i−1−i1−i−1+i22-2-22i2i−2i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i01+i−1−i1−i−1+i000−2ζ2ζ00−2ζ32ζ3−22−22−i2i2−i2i20000000000000000
χ312-22i−2i001+i−1−i1−i−1+i22-2-22i2i−2i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i-22−2i2i0−1−i1+i−1+i1−i02ζ−2ζ002ζ3−2ζ3002−2−22i2−i2−i2i20000000000000000
χ322-22i−2i001+i−1−i1−i−1+i22-2-22i2i−2i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i-22−2i2i0−1−i1+i−1+i1−i0−2ζ2ζ00−2ζ32ζ300−222−2−i2i2i2−i20000000000000000
χ332-22i−2i00−1−i1+i−1+i1−i22-2-22i2i−2i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i0−1−i1+i−1+i1−i0002ζ−2ζ002ζ3−2ζ3−22−22−i2i2−i2i20000000000000000
χ342-22i−2i00−1−i1+i−1+i1−i22-2-22i2i−2i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i0−1−i1+i−1+i1−i000−2ζ2ζ00−2ζ32ζ32−22−2i2−i2i2−i20000000000000000
χ352-22i−2i00−1−i1+i−1+i1−i22-2-22i2i−2i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i-22−2i2i01+i−1−i1−i−1+i02ζ−2ζ002ζ3−2ζ300−222−2−i2i2i2−i20000000000000000
χ362-22i−2i00−1−i1+i−1+i1−i22-2-22i2i−2i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i-22−2i2i01+i−1−i1−i−1+i0−2ζ2ζ00−2ζ32ζ3002−2−22i2−i2−i2i20000000000000000
χ372-2−2i2i001−i−1+i1+i−1−i22-2-2−2i−2i2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i01−i−1+i1+i−1−i0002ζ3−2ζ3002ζ−2ζ−22−22i2−i2i2−i20000000000000000
χ382-2−2i2i001−i−1+i1+i−1−i22-2-2−2i−2i2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i01−i−1+i1+i−1−i000−2ζ32ζ300−2ζ2ζ2−22−2−i2i2−i2i20000000000000000
χ392-2−2i2i001−i−1+i1+i−1−i22-2-2−2i−2i2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i-222i−2i0−1+i1−i−1−i1+i02ζ3−2ζ3002ζ−2ζ00−222−2i2−i2−i2i20000000000000000
χ402-2−2i2i001−i−1+i1+i−1−i22-2-2−2i−2i2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i-222i−2i0−1+i1−i−1−i1+i0−2ζ32ζ300−2ζ2ζ002−2−22−i2i2i2−i20000000000000000
χ412-2−2i2i00−1+i1−i−1−i1+i22-2-2−2i−2i2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i0−1+i1−i−1−i1+i0002ζ3−2ζ3002ζ−2ζ2−22−2−i2i2−i2i20000000000000000
χ422-2−2i2i00−1+i1−i−1−i1+i22-2-2−2i−2i2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i0−1+i1−i−1−i1+i000−2ζ32ζ300−2ζ2ζ−22−22i2−i2i2−i20000000000000000
χ432-2−2i2i00−1+i1−i−1−i1+i22-2-2−2i−2i2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i-222i−2i01−i−1+i1+i−1−i02ζ3−2ζ3002ζ−2ζ002−2−22−i2i2i2−i20000000000000000
χ442-2−2i2i00−1+i1−i−1−i1+i22-2-2−2i−2i2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i-222i−2i01−i−1+i1+i−1−i0−2ζ32ζ300−2ζ2ζ00−222−2i2−i2−i2i20000000000000000
χ4544444444441-21-21-21-21-21-21-21-21-21-200000000000000000000000000020200220-10-100-1-1
χ4644444444441-21-21-21-21-21-21-21-21-21-2000000000000000000000000000-20-200-2-201010011
χ474444444444-21-21-21-21-21-21-21-21-21-210000000000000000000000000020202200-10-10-1-100
χ484444444444-21-21-21-21-21-21-21-21-21-2100000000000000000000000000-20-20-2-20010101100
χ49444444-4-4-4-41-21-21-21-21-21-2-12-12-12-1200000000000000000000000000020200-2-20-10-10011
χ50444444-4-4-4-41-21-21-21-21-21-2-12-12-12-12000000000000000000000000000-20-20022010100-1-1
χ51444444-4-4-4-4-21-21-21-21-21-212-12-12-12-1000000000000000000000000002020-2-200-10-101100
χ52444444-4-4-4-4-21-21-21-21-21-212-12-12-12-100000000000000000000000000-20-2022001010-1-100
χ5344-4-4-444i4i−4i−4i1-21-2-12-12-121-2i−2ii−2i−i2i−i2i00000000000000000000000000020-2002i−2i0-10100−ii
χ5444-4-4-444i4i−4i−4i1-21-2-12-12-121-2i−2ii−2i−i2i−i2i000000000000000000000000000-20200−2i2i010-100i−i
χ5544-4-4-444i4i−4i−4i-21-212-12-12-1-21−2ii−2ii2i−i2i−i0000000000000000000000000020-202i−2i00-1010−ii00
χ5644-4-4-444i4i−4i−4i-21-212-12-12-1-21−2ii−2ii2i−i2i−i00000000000000000000000000-2020−2i2i0010-10i−i00
χ5744-4-4-44−4i−4i4i4i1-21-2-12-12-121-2−i2i−i2ii−2ii−2i00000000000000000000000000020-200−2i2i0-10100i−i
χ5844-4-4-44−4i−4i4i4i1-21-2-12-12-121-2−i2i−i2ii−2ii−2i000000000000000000000000000-202002i−2i010-100−ii
χ5944-4-4-44−4i−4i4i4i-21-212-12-12-1-212i−i2i−i−2ii−2ii0000000000000000000000000020-20−2i2i00-1010i−i00
χ6044-4-4-44−4i−4i4i4i-21-212-12-12-1-212i−i2i−i−2ii−2ii00000000000000000000000000-20202i−2i0010-10−ii00
χ618888-8-800002-42-42-42-4-24-2400000000000000000000000000000000000000000000000000
χ628888-8-80000-42-42-42-424-24-200000000000000000000000000000000000000000000000000
χ6388-8-88-800002-42-4-24-242-4-2400000000000000000000000000000000000000000000000000
χ6488-8-88-80000-42-424-24-2-424-200000000000000000000000000000000000000000000000000
χ658-88i−8i004+4i−4−4i4−4i−4+4i2-4-242i−4i−2i4i00001+i−2−2i−1−i2+2i1−i−2+2i−1+i2−2i000000000000000000000000000000000000000000
χ668-88i−8i004+4i−4−4i4−4i−4+4i-424-2−4i2i4i−2i0000−2−2i1+i2+2i−1−i−2+2i1−i2−2i−1+i000000000000000000000000000000000000000000
χ678-88i−8i00−4−4i4+4i−4+4i4−4i2-4-242i−4i−2i4i0000−1−i2+2i1+i−2−2i−1+i2−2i1−i−2+2i000000000000000000000000000000000000000000
χ688-88i−8i00−4−4i4+4i−4+4i4−4i-424-2−4i2i4i−2i00002+2i−1−i−2−2i1+i2−2i−1+i−2+2i1−i000000000000000000000000000000000000000000
χ698-8−8i8i004−4i−4+4i4+4i−4−4i2-4-24−2i4i2i−4i00001−i−2+2i−1+i2−2i1+i−2−2i−1−i2+2i000000000000000000000000000000000000000000
χ708-8−8i8i004−4i−4+4i4+4i−4−4i-424-24i−2i−4i2i0000−2+2i1−i2−2i−1+i−2−2i1+i2+2i−1−i000000000000000000000000000000000000000000
χ718-8−8i8i00−4+4i4−4i−4−4i4+4i2-4-24−2i4i2i−4i0000−1+i2−2i1−i−2+2i−1−i2+2i1+i−2−2i000000000000000000000000000000000000000000
χ728-8−8i8i00−4+4i4−4i−4−4i4+4i-424-24i−2i−4i2i00002−2i−1+i−2+2i1−i2+2i−1−i−2−2i1+i000000000000000000000000000000000000000000

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