Finite Group Databasebeta

← Group #11797692

Character table — Group #11797692

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222224444444488888888888899991818181818181818181818181818181818181818181824242424242424244848484848484848
order1222448888336666661212121224242424242424244444448888161616161616161616161616161616162244444466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111
χ911-1-1-11ii−i−i11-1-11-1-1111-1-1iiii−i−i−i−iii−i−ii−i11-1-11111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−i1-1i−ii−i1-1
χ1011-1-1-11ii−i−i11-1-11-1-1111-1-1iiii−i−i−i−iii−i−ii−i11-1-11111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii-11−ii−ii-11
χ1111-1-1-11ii−i−i11-1-11-1-1111-1-1iiii−i−i−i−iii−i−ii−i11-1-1-1-1-1-11111−i−i−i−iiiii1-1-11i−i−ii1-1i−i−ii-11
χ1211-1-1-11ii−i−i11-1-11-1-1111-1-1iiii−i−i−i−iii−i−ii−i11-1-1-1-1-1-11111−i−i−i−iiiii-111-1−iii−i-11−iii−i1-1
χ1311-1-1-11−i−iii11-1-11-1-1111-1-1−i−i−i−iiiii−i−iii−ii11-1-11111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii1-1−ii−ii1-1
χ1411-1-1-11−i−iii11-1-11-1-1111-1-1−i−i−i−iiiii−i−iii−ii11-1-11111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i-11i−ii−i-11
χ1511-1-1-11−i−iii11-1-11-1-1111-1-1−i−i−i−iiiii−i−iii−ii11-1-1-1-1-1-11111iiii−i−i−i−i1-1-11−iii−i1-1−iii−i-11
χ1611-1-1-11−i−iii11-1-11-1-1111-1-1−i−i−i−iiiii−i−iii−ii11-1-1-1-1-1-11111iiii−i−i−i−i-111-1i−i−ii-11i−i−ii1-1
χ17222222222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000000000
χ192222-2-2000022222222-2-2-2-2000000002222-2-2000022−2−222−2−222−2−222−2−20000000000000000
χ202222-2-2000022222222-2-2-2-2000000002222-2-20000−2−222−2−222−2−222−2−2220000000000000000
χ212222-2-2000022222222-2-2-2-200000000-2-2-2-222000022−2−222−2−2−2−222−2−2220000000000000000
χ222222-2-2000022222222-2-2-2-200000000-2-2-2-2220000−2−222−2−22222−2−222−2−20000000000000000
χ2322-2-22-2000022-2-22-2-22-2-222000000002i2i−2i−2i−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ2422-2-22-2000022-2-22-2-22-2-222000000002i2i−2i−2i−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2522-2-22-2000022-2-22-2-22-2-22200000000−2i−2i2i2i2i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ2622-2-22-2000022-2-22-2-22-2-22200000000−2i−2i2i2i2i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2722-2-2-222i2i−2i−2i22-2-22-2-2222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i−2i2i-2-22200000000000000000000000000000000
χ2822-2-2-22−2i−2i2i2i22-2-22-2-2222-2-2−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i2i−2i-2-22200000000000000000000000000000000
χ292-22-200i2−i2i2−i222-22-22-2-20000i2i2−i2−i2i2i2−i2−i22i−2i2i−2i002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ302-22-200i2−i2i2−i222-22-22-2-20000i2i2−i2−i2i2i2−i2−i22i−2i2i−2i002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ312-22-200i2−i2i2−i222-22-22-2-20000i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i00−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ322-22-200i2−i2i2−i222-22-22-2-20000i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i00−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ332-22-200−i2i2−i2i222-22-22-2-20000−i2−i2i2i2−i2−i2i2i22i−2i2i−2i00−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ342-22-200−i2i2−i2i222-22-22-2-20000−i2−i2i2i2−i2−i2i2i22i−2i2i−2i00−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ352-22-200−i2i2−i2i222-22-22-2-20000−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ362-22-200−i2i2−i2i222-22-22-2-20000−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ372-2-22002−2−22222-2-2-22-2000022−2−2−2−2222-2-22002−2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ382-2-22002−2−22222-2-2-22-2000022−2−2−2−2222-2-22002−2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ392-2-22002−2−22222-2-2-22-2000022−2−2−2−222-222-200−222−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ402-2-22002−2−22222-2-2-22-2000022−2−2−2−222-222-200−222−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ412-2-2200−222−2222-2-2-22-20000−2−22222−2−22-2-2200−222−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ422-2-2200−222−2222-2-2-22-20000−2−22222−2−22-2-2200−222−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ432-2-2200−222−2222-2-2-22-20000−2−22222−2−2-222-2002−2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ442-2-2200−222−2222-2-2-22-20000−2−22222−2−2-222-2002−2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ4544444444441-21-2-21-21-21-211-21-21-21-200000000000000000000000000002200220000-1-1-1-1
χ4644444444441-21-2-21-21-21-211-21-21-21-20000000000000000000000000000-2-200-2-200001111
χ474444444444-21-211-21-21-21-2-21-21-21-210000000000000000000000000022002200-1-1-1-10000
χ484444444444-21-211-21-21-21-2-21-21-21-2100000000000000000000000000-2-200-2-20011110000
χ49444444-4-4-4-41-21-2-21-21-21-21-12-12-12-1200000000000000000000000000002200-2-2000011-1-1
χ50444444-4-4-4-41-21-2-21-21-21-21-12-12-12-120000000000000000000000000000-2-200220000-1-111
χ51444444-4-4-4-4-21-211-21-21-21-22-12-12-12-1000000000000000000000000002200-2-200-1-1110000
χ52444444-4-4-4-4-21-211-21-21-21-22-12-12-12-100000000000000000000000000-2-200220011-1-10000
χ5344-4-4-444i4i−4i−4i1-2-12-2-121-212-1i−2ii−2i−i2i−i2i00000000000000000000000000002-2002i−2i0000−ii-11
χ5444-4-4-444i4i−4i−4i1-2-12-2-121-212-1i−2ii−2i−i2i−i2i0000000000000000000000000000-2200−2i2i0000i−i1-1
χ5544-4-4-444i4i−4i−4i-212-112-1-21-2-12−2ii−2ii2i−i2i−i000000000000000000000000002-2002i−2i00-11−ii0000
χ5644-4-4-444i4i−4i−4i-212-112-1-21-2-12−2ii−2ii2i−i2i−i00000000000000000000000000-2200−2i2i001-1i−i0000
χ5744-4-4-44−4i−4i4i4i1-2-12-2-121-212-1−i2i−i2ii−2ii−2i00000000000000000000000000002-200−2i2i0000i−i-11
χ5844-4-4-44−4i−4i4i4i1-2-12-2-121-212-1−i2i−i2ii−2ii−2i0000000000000000000000000000-22002i−2i0000−ii1-1
χ5944-4-4-44−4i−4i4i4i-212-112-1-21-2-122i−i2i−i−2ii−2ii000000000000000000000000002-200−2i2i00-11i−i0000
χ6044-4-4-44−4i−4i4i4i-212-112-1-21-2-122i−i2i−i−2ii−2ii00000000000000000000000000-22002i−2i001-1−ii0000
χ618888-8-800002-42-4-42-424-24-200000000000000000000000000000000000000000000000000
χ628888-8-80000-42-422-42-4-24-2400000000000000000000000000000000000000000000000000
χ6388-8-88-800002-4-24-4-2424-2-4200000000000000000000000000000000000000000000000000
χ6488-8-88-80000-424-224-2-4-242-400000000000000000000000000000000000000000000000000
χ658-88-8004i2−4i24i2−4i22-4-2-4424-20000i2−2i2−i22i2i2−2i2−i22i2000000000000000000000000000000000000000000
χ668-88-8004i2−4i24i2−4i2-4242-2-4-240000−2i2i22i2−i2−2i2i22i2−i2000000000000000000000000000000000000000000
χ678-88-800−4i24i2−4i24i22-4-2-4424-20000−i22i2i2−2i2−i22i2i2−2i2000000000000000000000000000000000000000000
χ688-88-800−4i24i2−4i24i2-4242-2-4-2400002i2−i2−2i2i22i2−i2−2i2i2000000000000000000000000000000000000000000
χ698-8-880042−42−42422-4244-2-4-200002−22−222−2222−22000000000000000000000000000000000000000000
χ708-8-880042−42−4242-42-4-2-24240000−22222−222−2−222000000000000000000000000000000000000000000
χ718-8-8800−424242−422-4244-2-4-20000−2222−222−22−222000000000000000000000000000000000000000000
χ728-8-8800−424242−42-42-4-2-2424000022−2−222−22222−2000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.