Finite Group Databasebeta

← Group #72220463

Character table — Group #72220463

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222288889999161616161616181818181818181818183636363636363636363636363636363636363636363648484848727272727272727296969696
order1244244444361212224461212121212244444444444444444444444444444442488888888886122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111-1-1-1-11111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111-1-1-1-11111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1
χ8111111-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111
χ911-1-1-11ii−i−i11-1-111-1-1-11ii−i−i-11ii−i−i11-1-11-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ1011-1-1-11ii−i−i11-1-111-1-1-11ii−i−i-11ii−i−i11-1-11-11111-1-1-1-1ii−i−iiiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ1111-1-1-11ii−i−i11-1-111-1-1-11ii−i−i-11ii−i−i11-1-11-1-1-1-1-11111ii−i−i−i−i−i−iiiii1-1i−i-1-111−i−iii1-1i−i
χ1211-1-1-11ii−i−i11-1-111-1-1-11ii−i−i-11ii−i−i11-1-11-1-1-1-1-11111ii−i−i−i−i−i−iiiii-11−ii11-1-1ii−i−i-11−ii
χ1311-1-1-11−i−iii11-1-111-1-1-11−i−iii-11−i−iii11-1-11-11111-1-1-1-1−i−iii−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ1411-1-1-11−i−iii11-1-111-1-1-11−i−iii-11−i−iii11-1-11-11111-1-1-1-1−i−iii−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ1511-1-1-11−i−iii11-1-111-1-1-11−i−iii-11−i−iii11-1-11-1-1-1-1-11111−i−iiiiiii−i−i−i−i1-1−ii-1-111ii−i−i1-1−ii
χ1611-1-1-11−i−iii11-1-111-1-1-11−i−iii-11−i−iii11-1-11-1-1-1-1-11111−i−iiiiiii−i−i−i−i-11i−i11-1-1−i−iii-11i−i
χ17222222222222222222222222222222-2-2-2-2-2-200000000-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ1922222222222222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ20222222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000
χ21222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-22222000000000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ22222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-22222000000000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ232222-2-2000022222222-2-20000-2-200002222-2-222-2-222-2-20000000000000000000000000000
χ242222-2-2000022222222-2-20000-2-200002222-2-2-2-222-2-2220000000000000000000000000000
χ252222-2-2000022222222-2-20000-2-20000-2-2-2-2220000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ262222-2-2000022222222-2-20000-2-20000-2-2-2-222000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722-2-22-2000022-2-222-2-22-200002-2000022-2-2-2222-2-2-2-2220000000000000000000000000000
χ2822-2-22-2000022-2-222-2-22-200002-2000022-2-2-22-2-22222-2-20000000000000000000000000000
χ2922-2-22-2000022-2-222-2-22-200002-20000-2-2222-200000000000022-2-2-2-2220000000000000000
χ3022-2-22-2000022-2-222-2-22-200002-20000-2-2222-2000000000000-2-22222-2-20000000000000000
χ3122-2-2-222i2i−2i−2i22-2-222-2-2-222i2i−2i−2i-222i2i−2i−2i-2-222-2200000000−2i−2i2i2i000000000000000000000000
χ3222-2-2-222i2i−2i−2i22-2-2-2-222-222i2i−2i−2i2-2−2i−2i2i2i000000000000000000000000000000i2−i2−i2i2−222−20000
χ3322-2-2-222i2i−2i−2i22-2-2-2-222-222i2i−2i−2i2-2−2i−2i2i2i000000000000000000000000000000−i2i2i2−i22−2−220000
χ3422-2-2-22−2i−2i2i2i22-2-222-2-2-22−2i−2i2i2i-22−2i−2i2i2i-2-222-22000000002i2i−2i−2i000000000000000000000000
χ3522-2-2-22−2i−2i2i2i22-2-2-2-222-22−2i−2i2i2i2-22i2i−2i−2i000000000000000000000000000000i2−i2−i2i22−2−220000
χ3622-2-2-22−2i−2i2i2i22-2-2-2-222-22−2i−2i2i2i2-22i2i−2i−2i000000000000000000000000000000−i2i2i2−i2−222−20000
χ372-22i−2i001+i−1−i1−i−1+i2-22i−2i2-22i−2i001+i−1−i1−i−1+i001+i−1−i1−i−1+i2-22i−2i00002i−2i002-21+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ382-22i−2i001+i−1−i1−i−1+i2-22i−2i2-22i−2i001+i−1−i1−i−1+i001+i−1−i1−i−1+i2-22i−2i0000−2i2i00-221+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ392-22i−2i001+i−1−i1−i−1+i2-22i−2i2-22i−2i001+i−1−i1−i−1+i001+i−1−i1−i−1+i-22−2i2i002-2002i−2i00−1−i1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ402-22i−2i001+i−1−i1−i−1+i2-22i−2i2-22i−2i001+i−1−i1−i−1+i001+i−1−i1−i−1+i-22−2i2i00-2200−2i2i00−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ412-22i−2i00−1−i1+i−1+i1−i2-22i−2i2-22i−2i00−1−i1+i−1+i1−i00−1−i1+i−1+i1−i2-22i−2i00002i−2i002-2−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ422-22i−2i00−1−i1+i−1+i1−i2-22i−2i2-22i−2i00−1−i1+i−1+i1−i00−1−i1+i−1+i1−i2-22i−2i0000−2i2i00-22−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ432-22i−2i00−1−i1+i−1+i1−i2-22i−2i2-22i−2i00−1−i1+i−1+i1−i00−1−i1+i−1+i1−i-22−2i2i002-2002i−2i001+i−1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ442-22i−2i00−1−i1+i−1+i1−i2-22i−2i2-22i−2i00−1−i1+i−1+i1−i00−1−i1+i−1+i1−i-22−2i2i00-2200−2i2i001+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ452-2−2i2i001−i−1+i1+i−1−i2-2−2i2i2-2−2i2i001−i−1+i1+i−1−i001−i−1+i1+i−1−i2-2−2i2i00002i−2i00-221−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ462-2−2i2i001−i−1+i1+i−1−i2-2−2i2i2-2−2i2i001−i−1+i1+i−1−i001−i−1+i1+i−1−i2-2−2i2i0000−2i2i002-21−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ472-2−2i2i001−i−1+i1+i−1−i2-2−2i2i2-2−2i2i001−i−1+i1+i−1−i001−i−1+i1+i−1−i-222i−2i002-200−2i2i00−1+i1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ482-2−2i2i001−i−1+i1+i−1−i2-2−2i2i2-2−2i2i001−i−1+i1+i−1−i001−i−1+i1+i−1−i-222i−2i00-22002i−2i00−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ492-2−2i2i00−1+i1−i−1−i1+i2-2−2i2i2-2−2i2i00−1+i1−i−1−i1+i00−1+i1−i−1−i1+i2-2−2i2i00002i−2i00-22−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ502-2−2i2i00−1+i1−i−1−i1+i2-2−2i2i2-2−2i2i00−1+i1−i−1−i1+i00−1+i1−i−1−i1+i2-2−2i2i0000−2i2i002-2−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ512-2−2i2i00−1+i1−i−1−i1+i2-2−2i2i2-2−2i2i00−1+i1−i−1−i1+i00−1+i1−i−1−i1+i-222i−2i002-200−2i2i001−i−1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ522-2−2i2i00−1+i1−i−1−i1+i2-2−2i2i2-2−2i2i00−1+i1−i−1−i1+i00−1+i1−i−1−i1+i-222i−2i00-22002i−2i001−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ534444-4-400004444-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ5444-4-44-4000044-4-4-4-4444-40000-440000000000000000000000000000000000000000000000
χ554-44i−4i002+2i−2−2i2−2i−2+2i4-44i−4i-44−4i4i002+2i−2−2i2−2i−2+2i00−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000000000
χ564-44i−4i00−2−2i2+2i−2+2i2−2i4-44i−4i-44−4i4i00−2−2i2+2i−2+2i2−2i002+2i−2−2i2−2i−2+2i000000000000000000000000000000000000000000
χ574-4−4i4i002−2i−2+2i2+2i−2−2i4-4−4i4i-444i−4i002−2i−2+2i2+2i−2−2i00−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000000000
χ584-4−4i4i00−2+2i2−2i−2−2i2+2i4-4−4i4i-444i−4i00−2+2i2−2i−2−2i2+2i002−2i−2+2i2+2i−2−2i000000000000000000000000000000000000000000
χ598888888888-1-1-1-10000-1-1-1-1-1-100000000000000000000000000000000222200000000-1-1-1-1
χ608888888888-1-1-1-10000-1-1-1-1-1-100000000000000000000000000000000-2-2-2-2000000001111
χ61888888-8-8-8-8-1-1-1-10000-1-111110000000000000000000000000000000022-2-200000000-1-111
χ62888888-8-8-8-8-1-1-1-10000-1-1111100000000000000000000000000000000-2-2220000000011-1-1
χ6388-8-8-888i8i−8i−8i-1-11100001-1−i−iii000000000000000000000000000000002-22i−2i00000000-11−ii
χ6488-8-8-888i8i−8i−8i-1-11100001-1−i−iii00000000000000000000000000000000-22−2i2i000000001-1i−i
χ6588-8-8-88−8i−8i8i8i-1-11100001-1ii−i−i000000000000000000000000000000002-2−2i2i00000000-11i−i
χ6688-8-8-88−8i−8i8i8i-1-11100001-1ii−i−i00000000000000000000000000000000-222i−2i000000001-1−ii
χ6716161616-16-160000-2-2-2-20000220000000000000000000000000000000000000000000000000000
χ681616-16-1616-160000-2-2220000-220000000000000000000000000000000000000000000000000000
χ6916-1616i−16i008+8i−8−8i8−8i−8+8i-22−2i2i000000−1−i1+i−1+i1−i000000000000000000000000000000000000000000000000
χ7016-1616i−16i00−8−8i8+8i−8+8i8−8i-22−2i2i0000001+i−1−i1−i−1+i000000000000000000000000000000000000000000000000
χ7116-16−16i16i008−8i−8+8i8+8i−8−8i-222i−2i000000−1+i1−i−1−i1+i000000000000000000000000000000000000000000000000
χ7216-16−16i16i00−8+8i8−8i−8−8i8+8i-222i−2i0000001−i−1+i1+i−1−i000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).