Finite Group Databasebeta

← Group #11771644

Character table — Group #11771644

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222244444444888888888888889999161616161616161618181818181818181818181818181818181818181818727272727272
order1244248888336612121212246612122424242424242424888866661212121244448888888888888888888816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1ii−i−i
χ411111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1−i−iii
χ5111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1
χ6111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11−i−iii
χ8111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11ii−i−i
χ911-1-1-1111-1-11111-1-1-1-11-1-1-1111111-1-1-1-1ii−i−i1111-1-1-1-1ii−i−ii−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3i−iζ−ζζ3−ζ3
χ1011-1-1-1111-1-11111-1-1-1-11-1-1-1111111-1-1-1-1ii−i−i1111-1-1-1-1ii−i−ii−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3i−i−ζζ−ζ3ζ3
χ1111-1-1-1111-1-11111-1-1-1-11-1-1-1111111-1-1-1-1−i−iii1111-1-1-1-1−i−iii−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−iiζ3−ζ3ζ−ζ
χ1211-1-1-1111-1-11111-1-1-1-11-1-1-1111111-1-1-1-1−i−iii1111-1-1-1-1−i−iii−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ii−ζ3ζ3−ζζ
χ1311-1-1-1111-1-11111-1-1-1-1-11-1-1111111-1-1-1-1ii−i−i-1-1-1-11111ii−i−ii−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ii−ζζ−ζ3ζ3
χ1411-1-1-1111-1-11111-1-1-1-1-11-1-1111111-1-1-1-1ii−i−i-1-1-1-11111ii−i−ii−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−iiζ−ζζ3−ζ3
χ1511-1-1-1111-1-11111-1-1-1-1-11-1-1111111-1-1-1-1−i−iii-1-1-1-11111−i−iii−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζi−i−ζ3ζ3−ζζ
χ1611-1-1-1111-1-11111-1-1-1-1-11-1-1111111-1-1-1-1−i−iii-1-1-1-11111−i−iii−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζi−iζ3−ζ3ζ−ζ
χ17222222-2-2-2-222222222002222-2-2-2-2-2-2-2-2222200000000-2-2-2-2220000000000000000000000
χ18222222-2-2-2-222222222002222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-20000000000000000000000
χ192222-2-200002222222200-2-2-2-2000000002222000000000000-2-222−2−222−2−222−2−222−2−2000000
χ202222-2-200002222222200-2-2-2-2000000002222000000000000-2-2−2−222−2−222−2−222−2−222000000
χ212222-2-200002222222200-2-2-2-200000000-2-2-2-200000000000022i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000
χ222222-2-200002222222200-2-2-2-200000000-2-2-2-200000000000022−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000
χ2322-2-22-200002222-2-2-2-20022-2-2000000002i2i−2i−2i000000000000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000
χ2422-2-22-200002222-2-2-2-20022-2-2000000002i2i−2i−2i000000000000−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000
χ2522-2-22-200002222-2-2-2-20022-2-200000000−2i−2i2i2i0000000000002i−2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000
χ2622-2-22-200002222-2-2-2-20022-2-200000000−2i−2i2i2i0000000000002i−2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000
χ2722-2-2-22-2-2222222-2-2-2-200-2-222-2-2-2-222222i2i−2i−2i00000000−2i−2i2i2i2i−2i0000000000000000000000
χ2822-2-2-22-2-2222222-2-2-2-200-2-222-2-2-2-22222−2i−2i2i2i000000002i2i−2i−2i−2i2i0000000000000000000000
χ292-22i−2i002−2i2−i222-2-22i2i−2i−2i00000022−2−2i2i2−i2−i22ζ−2ζ2ζ3−2ζ3000000001+i−1−i1−i−1+i001+ζ−1−ζi−ζ3−i+ζ3i+ζ3−i−ζ31−ζ−1+ζζ+i−ζ−i1+ζ3−1−ζ31−ζ3−1+ζ3ζ−i−ζ+i000000
χ302-22i−2i002−2i2−i222-2-22i2i−2i−2i00000022−2−2i2i2−i2−i22ζ−2ζ2ζ3−2ζ3000000001+i−1−i1−i−1+i00−1−ζ1+ζ−i+ζ3i−ζ3−i−ζ3i+ζ3−1+ζ1−ζ−ζ−iζ+i−1−ζ31+ζ3−1+ζ31−ζ3−ζ+iζ−i000000
χ312-22i−2i002−2i2−i222-2-22i2i−2i−2i00000022−2−2i2i2−i2−i2−2ζ2ζ−2ζ32ζ300000000−1−i1+i−1+i1−i00i+ζ3−i−ζ3−1+ζ1−ζ−1−ζ1+ζi−ζ3−i+ζ31−ζ3−1+ζ3ζ−i−ζ+i−ζ−iζ+i−1−ζ31+ζ3000000
χ322-22i−2i002−2i2−i222-2-22i2i−2i−2i00000022−2−2i2i2−i2−i2−2ζ2ζ−2ζ32ζ300000000−1−i1+i−1+i1−i00−i−ζ3i+ζ31−ζ−1+ζ1+ζ−1−ζ−i+ζ3i−ζ3−1+ζ31−ζ3−ζ+iζ−iζ+i−ζ−i1+ζ3−1−ζ3000000
χ332-22i−2i00−22−i2i222-2-22i2i−2i−2i000000−2−222−i2−i2i2i22ζ−2ζ2ζ3−2ζ300000000−1−i1+i−1+i1−i00i−ζ3−i+ζ3−1−ζ1+ζ−1+ζ1−ζi+ζ3−i−ζ31+ζ3−1−ζ3−ζ−iζ+iζ−i−ζ+i−1+ζ31−ζ3000000
χ342-22i−2i00−22−i2i222-2-22i2i−2i−2i000000−2−222−i2−i2i2i22ζ−2ζ2ζ3−2ζ300000000−1−i1+i−1+i1−i00−i+ζ3i−ζ31+ζ−1−ζ1−ζ−1+ζ−i−ζ3i+ζ3−1−ζ31+ζ3ζ+i−ζ−i−ζ+iζ−i1−ζ3−1+ζ3000000
χ352-22i−2i00−22−i2i222-2-22i2i−2i−2i000000−2−222−i2−i2i2i2−2ζ2ζ−2ζ32ζ3000000001+i−1−i1−i−1+i001−ζ−1+ζi+ζ3−i−ζ3i−ζ3−i+ζ31+ζ−1−ζ−ζ+iζ−i1−ζ3−1+ζ31+ζ3−1−ζ3−ζ−iζ+i000000
χ362-22i−2i00−22−i2i222-2-22i2i−2i−2i000000−2−222−i2−i2i2i2−2ζ2ζ−2ζ32ζ3000000001+i−1−i1−i−1+i00−1+ζ1−ζ−i−ζ3i+ζ3−i+ζ3i−ζ3−1−ζ1+ζζ−i−ζ+i−1+ζ31−ζ3−1−ζ31+ζ3ζ+i−ζ−i000000
χ372-2−2i2i002−2−i2i222-2-2−2i−2i2i2i00000022−2−2−i2−i2i2i22ζ3−2ζ32ζ−2ζ00000000−1+i1−i−1−i1+i00ζ+i−ζ−i1+ζ3−1−ζ31−ζ3−1+ζ3−ζ+iζ−i−1−ζ1+ζ−i+ζ3i−ζ3−i−ζ3i+ζ31−ζ−1+ζ000000
χ382-2−2i2i002−2−i2i222-2-2−2i−2i2i2i00000022−2−2−i2−i2i2i22ζ3−2ζ32ζ−2ζ00000000−1+i1−i−1−i1+i00−ζ−iζ+i−1−ζ31+ζ3−1+ζ31−ζ3ζ−i−ζ+i1+ζ−1−ζi−ζ3−i+ζ3i+ζ3−i−ζ3−1+ζ1−ζ000000
χ392-2−2i2i002−2−i2i222-2-2−2i−2i2i2i00000022−2−2−i2−i2i2i2−2ζ32ζ3−2ζ2ζ000000001−i−1+i1+i−1−i001−ζ3−1+ζ3ζ−i−ζ+i−ζ−iζ+i1+ζ3−1−ζ3−i−ζ3i+ζ31−ζ−1+ζ1+ζ−1−ζi−ζ3−i+ζ3000000
χ402-2−2i2i002−2−i2i222-2-2−2i−2i2i2i00000022−2−2−i2−i2i2i2−2ζ32ζ3−2ζ2ζ000000001−i−1+i1+i−1−i00−1+ζ31−ζ3−ζ+iζ−iζ+i−ζ−i−1−ζ31+ζ3i+ζ3−i−ζ3−1+ζ1−ζ−1−ζ1+ζ−i+ζ3i−ζ3000000
χ412-2−2i2i00−22i2−i222-2-2−2i−2i2i2i000000−2−222i2i2−i2−i22ζ3−2ζ32ζ−2ζ000000001−i−1+i1+i−1−i001+ζ3−1−ζ3−ζ−iζ+iζ−i−ζ+i1−ζ3−1+ζ3−i+ζ3i−ζ31+ζ−1−ζ1−ζ−1+ζi+ζ3−i−ζ3000000
χ422-2−2i2i00−22i2−i222-2-2−2i−2i2i2i000000−2−222i2i2−i2−i22ζ3−2ζ32ζ−2ζ000000001−i−1+i1+i−1−i00−1−ζ31+ζ3ζ+i−ζ−i−ζ+iζ−i−1+ζ31−ζ3i−ζ3−i+ζ3−1−ζ1+ζ−1+ζ1−ζ−i−ζ3i+ζ3000000
χ432-2−2i2i00−22i2−i222-2-2−2i−2i2i2i000000−2−222i2i2−i2−i2−2ζ32ζ3−2ζ2ζ00000000−1+i1−i−1−i1+i00ζ−i−ζ+i−1+ζ31−ζ3−1−ζ31+ζ3−ζ−iζ+i1−ζ−1+ζi+ζ3−i−ζ3i−ζ3−i+ζ3−1−ζ1+ζ000000
χ442-2−2i2i00−22i2−i222-2-2−2i−2i2i2i000000−2−222i2i2−i2−i2−2ζ32ζ3−2ζ2ζ00000000−1+i1−i−1−i1+i00−ζ+iζ−i1−ζ3−1+ζ31+ζ3−1−ζ3ζ+i−ζ−i−1+ζ1−ζ−i−ζ3i+ζ3−i+ζ3i−ζ31+ζ−1−ζ000000
χ4544444444441-21-21-21-2441-21-21-21-21-21-2000011-2-211-2-20000000000000000000000000000
χ4644444444441-21-21-21-2-4-41-21-21-21-21-21-20000-1-122-1-1220000000000000000000000000000
χ474444444444-21-21-21-2144-21-21-21-21-21-210000-2-211-2-2110000000000000000000000000000
χ484444444444-21-21-21-21-4-4-21-21-21-21-21-21000022-1-122-1-10000000000000000000000000000
χ49444444-4-4-4-41-21-21-21-2001-21-2-12-12-12-1200003-3003-3000000000000000000000000000000
χ50444444-4-4-4-41-21-21-21-2001-21-2-12-12-12-120000-3300-33000000000000000000000000000000
χ51444444-4-4-4-4-21-21-21-2100-21-212-12-12-12-10000003-3003-30000000000000000000000000000
χ52444444-4-4-4-4-21-21-21-2100-21-212-12-12-12-1000000-3300-330000000000000000000000000000
χ5344-4-4-4444-4-41-21-2-12-124-4-121-21-21-2-12-12000011-2-2-1-1220000000000000000000000000000
χ5444-4-4-4444-4-41-21-2-12-12-44-121-21-21-2-12-120000-1-12211-2-20000000000000000000000000000
χ5544-4-4-4444-4-4-21-212-12-14-42-1-21-21-212-12-10000-2-21122-1-10000000000000000000000000000
χ5644-4-4-4444-4-4-21-212-12-1-442-1-21-21-212-12-1000022-1-1-2-2110000000000000000000000000000
χ5744-4-4-44-4-4441-21-2-12-1200-121-2-12-121-21-200003-300-33000000000000000000000000000000
χ5844-4-4-44-4-4441-21-2-12-1200-121-2-12-121-21-20000-33003-3000000000000000000000000000000
χ5944-4-4-44-4-444-21-212-12-1002-1-212-12-1-21-210000003-300-330000000000000000000000000000
χ6044-4-4-44-4-444-21-212-12-1002-1-212-12-1-21-21000000-33003-30000000000000000000000000000
χ618888-8-800002-42-42-42-400-24-24000000000000000000000000000000000000000000000000
χ628888-8-80000-42-42-42-42004-24-2000000000000000000000000000000000000000000000000
χ6388-8-88-800002-42-4-24-24002-4-24000000000000000000000000000000000000000000000000
χ6488-8-88-80000-42-424-24-200-424-2000000000000000000000000000000000000000000000000
χ658-88i−8i0042−424i2−4i22-4-242i−4i−2i4i0000002−22−222i2−2i2−i22i20000000000000000000000000000000000000000
χ668-88i−8i0042−424i2−4i2-424-2−4i2i4i−2i000000−22222−2−2i2i22i2−i20000000000000000000000000000000000000000
χ678-88i−8i00−4242−4i24i22-4-242i−4i−2i4i000000−2222−22−i22i2i2−2i20000000000000000000000000000000000000000
χ688-88i−8i00−4242−4i24i2-424-2−4i2i4i−2i00000022−2−2222i2−i2−2i2i20000000000000000000000000000000000000000
χ698-8−8i8i0042−42−4i24i22-4-24−2i4i2i−4i0000002−22−222−i22i2i2−2i20000000000000000000000000000000000000000
χ708-8−8i8i0042−42−4i24i2-424-24i−2i−4i2i000000−22222−22i2−i2−2i2i20000000000000000000000000000000000000000
χ718-8−8i8i00−42424i2−4i22-4-24−2i4i2i−4i000000−2222−22i2−2i2−i22i20000000000000000000000000000000000000000
χ728-8−8i8i00−42424i2−4i2-424-24i−2i−4i2i00000022−2−222−2i2i22i2−i20000000000000000000000000000000000000000

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