Finite Group Databasebeta

← Group #11796776

Character table — Group #11796776

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222224444444488888888888899991818181818181818181818181818181818181818181824242424242424244848484848484848
order124424888833661212121266121224242424242424242244248888161616161616161616161616161616162244888866121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-111-1-11-11-111-1-1
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11-1-111
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-1-1-1111-11-1-1-111
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1111-1-1-11-1111-1-1
χ911-1-1-1111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1i−ii−i11-1-1i−ii−i
χ1011-1-1-1111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−ii−ii-1-111−ii−ii
χ1111-1-1-1111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−ii−ii11-1-1−ii−ii
χ1211-1-1-1111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111i−ii−i-1-111i−ii−i
χ1311-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1111-111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii1-1-11i−i−ii
χ1411-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1111-111-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i-111-1−iii−i
χ1511-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1111-111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i1-1-11−iii−i
χ1611-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1111-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii-111-1i−i−ii
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
χ2322-2-22-200002222-2-2-2-222-2-20000000022-2-22-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2422-2-22-200002222-2-2-2-222-2-20000000022-2-22-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2522-2-22-200002222-2-2-2-222-2-200000000-2-222-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2622-2-22-200002222-2-2-2-222-2-200000000-2-222-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2722-2-2-2222-2-22222-2-2-2-2-2-2222222-2-2-2-2-2-2222-2-2-22200000000000000000000000000000000
χ2822-2-2-22-2-2222222-2-2-2-2-2-222-2-2-2-2222222-2-2-22-2-22200000000000000000000000000000000
χ292-22i−2i002−2i2−i222-2-22i−2i2i−2i000022−2−2i2i2−i2−i22-22i−2i002−2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000000000
χ302-22i−2i002−2i2−i222-2-22i−2i2i−2i000022−2−2i2i2−i2−i22-22i−2i002−2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000000000
χ312-22i−2i002−2i2−i222-2-22i−2i2i−2i000022−2−2i2i2−i2−i2-22−2i2i00−22−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000000000
χ322-22i−2i002−2i2−i222-2-22i−2i2i−2i000022−2−2i2i2−i2−i2-22−2i2i00−22−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000000000
χ332-22i−2i00−22−i2i222-2-22i−2i2i−2i0000−2−222−i2−i2i2i22-22i−2i00−22−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000000000
χ342-22i−2i00−22−i2i222-2-22i−2i2i−2i0000−2−222−i2−i2i2i22-22i−2i00−22−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000000000
χ352-22i−2i00−22−i2i222-2-22i−2i2i−2i0000−2−222−i2−i2i2i2-22−2i2i002−2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000000000
χ362-22i−2i00−22−i2i222-2-22i−2i2i−2i0000−2−222−i2−i2i2i2-22−2i2i002−2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000000000
χ372-2−2i2i002−2−i2i222-2-2−2i2i−2i2i000022−2−2−i2−i2i2i22-2−2i2i002−2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000000000
χ382-2−2i2i002−2−i2i222-2-2−2i2i−2i2i000022−2−2−i2−i2i2i22-2−2i2i002−2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000000000
χ392-2−2i2i002−2−i2i222-2-2−2i2i−2i2i000022−2−2−i2−i2i2i2-222i−2i00−22i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000000000
χ402-2−2i2i002−2−i2i222-2-2−2i2i−2i2i000022−2−2−i2−i2i2i2-222i−2i00−22i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000000000
χ412-2−2i2i00−22i2−i222-2-2−2i2i−2i2i0000−2−222i2i2−i2−i22-2−2i2i00−22i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000000000
χ422-2−2i2i00−22i2−i222-2-2−2i2i−2i2i0000−2−222i2i2−i2−i22-2−2i2i00−22i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000000000
χ432-2−2i2i00−22i2−i222-2-2−2i2i−2i2i0000−2−222i2i2−i2−i2-222i−2i002−2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000000000
χ442-2−2i2i00−22i2−i222-2-2−2i2i−2i2i0000−2−222i2i2−i2−i2-222i−2i002−2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000000000
χ4544444444441-21-2-2-2111-21-21-21-21-21-200000000000000000000000000000022220000-1-1-1-1
χ4644444444441-21-2-2-2111-21-21-21-21-21-2000000000000000000000000000000-2-2-2-200001111
χ474444444444-21-2111-2-2-21-21-21-21-21-210000000000000000000000000022220000-1-1-1-10000
χ484444444444-21-2111-2-2-21-21-21-21-21-2100000000000000000000000000-2-2-2-2000011110000
χ49444444-4-4-4-41-21-2-2-2111-21-2-12-12-12-1200000000000000000000000000000022-2-20000-1-111
χ50444444-4-4-4-41-21-2-2-2111-21-2-12-12-12-12000000000000000000000000000000-2-222000011-1-1
χ51444444-4-4-4-4-21-2111-2-2-21-212-12-12-12-1000000000000000000000000002-22-20000-11-110000
χ52444444-4-4-4-4-21-2111-2-2-21-212-12-12-12-100000000000000000000000000-22-2200001-11-10000
χ5344-4-4-4444-4-41-21-222-1-1-121-21-21-2-12-120000000000000000000000000000002i−2i2i−2i0000−ii−ii
χ5444-4-4-4444-4-41-21-222-1-1-121-21-21-2-12-12000000000000000000000000000000−2i2i−2i2i0000i−ii−i
χ5544-4-4-4444-4-4-21-21-1-1222-1-21-21-212-12-10000000000000000000000000022-2-20000-1-1110000
χ5644-4-4-4444-4-4-21-21-1-1222-1-21-21-212-12-100000000000000000000000000-2-222000011-1-10000
χ5744-4-4-44-4-4441-21-222-1-1-121-2-12-121-21-20000000000000000000000000000002i−2i−2i2i0000−iii−i
χ5844-4-4-44-4-4441-21-222-1-1-121-2-12-121-21-2000000000000000000000000000000−2i2i2i−2i0000i−i−ii
χ5944-4-4-44-4-444-21-21-1-1222-1-212-12-1-21-21000000000000000000000000002-2-220000-111-10000
χ6044-4-4-44-4-444-21-21-1-1222-1-212-12-1-21-2100000000000000000000000000-222-200001-1-110000
χ618888-8-800002-42-4-4-422-24-2400000000000000000000000000000000000000000000000000
χ628888-8-80000-42-4222-4-44-24-200000000000000000000000000000000000000000000000000
χ6388-8-88-800002-42-444-2-22-4-2400000000000000000000000000000000000000000000000000
χ6488-8-88-80000-42-42-2-244-424-200000000000000000000000000000000000000000000000000
χ658-88i−8i0042−424i2−4i22-4-24−4i4i2i−2i00002−22−222i2−2i2−i22i2000000000000000000000000000000000000000000
χ668-88i−8i0042−424i2−4i2-424-22i−2i−4i4i0000−22222−2−2i2i22i2−i2000000000000000000000000000000000000000000
χ678-88i−8i00−4242−4i24i22-4-24−4i4i2i−2i0000−2222−22−i22i2i2−2i2000000000000000000000000000000000000000000
χ688-88i−8i00−4242−4i24i2-424-22i−2i−4i4i000022−2−2222i2−i2−2i2i2000000000000000000000000000000000000000000
χ698-8−8i8i0042−42−4i24i22-4-244i−4i−2i2i00002−22−222−i22i2i2−2i2000000000000000000000000000000000000000000
χ708-8−8i8i0042−42−4i24i2-424-2−2i2i4i−4i0000−22222−22i2−i2−2i2i2000000000000000000000000000000000000000000
χ718-8−8i8i00−42424i2−4i22-4-244i−4i−2i2i0000−2222−22i2−2i2−i22i2000000000000000000000000000000000000000000
χ728-8−8i8i00−42424i2−4i2-424-2−2i2i4i−4i000022−2−222−2i2i22i2−i2000000000000000000000000000000000000000000

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