Finite Group Databasebeta

← Group #97488

Character table — Group #97488

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222222244444444444444448888888888888888224444444444244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-111-1-11-1-11-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-11-1-111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-111-1-1-11ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-11111-11-111-1−i−iiiii−i−i−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1-1-1111-11-11-1−i−iii−i−iiiii−i−i
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-11111-1-1-1-111-11ii−i−i−i−iii−i−iii
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-111-1-1-11−i−iii−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-11111-11-111-1ii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1-1-1111-11-11-1ii−i−iii−i−i−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-11111-1-1-1-111-11−i−iiiii−i−iii−i−i
χ1722222222222222-2-222-2-2-2-2-222-2-2-20000000000000000000022002200-200-200000000000000
χ1822222222222222-2-222-2-2-2-2-222-2-2-200000000000000000000-2-200-2-200200200000000000000
χ19222222222222-2-222-2-222-2-2-2-2-222-200000000000000002222000000000-2-2000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-222-20000000000000000-2-2-2-200000000022000000000000000
χ21222222222222-2-2-2-2-2-2-2-2222-2-2-2-2200000000000000000000002200-2-200002-2000000000000
χ22222222222222-2-2-2-2-2-2-2-2222-2-2-2-220000000000000000000000-2-200220000-22000000000000
χ2322222222-2-2-2-22222222222-2-2-2-2-2-200000000000000000000002200220000-2-2000000000000
χ2422222222-2-2-2-22222222222-2-2-2-2-2-20000000000000000000000-2-200-2-2000022000000000000
χ2522222222-2-2-2-222-2-222-2-2-2-22-2-2222000000000000000022-2-2000000000-22000000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-22-2-22220000000000000000-2-2220000000002-2000000000000000
χ2722222222-2-2-2-2-2-222-2-222-2-2222-2-22000000000000000000002200-2-200-200200000000000000
χ2822222222-2-2-2-2-2-222-2-222-2-2222-2-2200000000000000000000-2-2002200200-200000000000000
χ292-222-2-22-200002i−2i2i−2i2i−2i2i−2i2-20000001+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i0000002-2002i−2i0000001+i−1−i1−i−1+i00000000
χ302-222-2-22-200002i−2i2i−2i2i−2i2i−2i2-20000001+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i000000-2200−2i2i000000−1−i1+i−1+i1−i00000000
χ312-222-2-22-200002i−2i2i−2i2i−2i2i−2i2-2000000−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i0000002-2002i−2i000000−1−i1+i−1+i1−i00000000
χ322-222-2-22-200002i−2i2i−2i2i−2i2i−2i2-2000000−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i000000-2200−2i2i0000001+i−1−i1−i−1+i00000000
χ332-222-2-22-20000−2i2i−2i2i−2i2i−2i2i2-20000001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i0000002-200−2i2i0000001−i−1+i1+i−1−i00000000
χ342-222-2-22-20000−2i2i−2i2i−2i2i−2i2i2-20000001−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i000000-22002i−2i000000−1+i1−i−1−i1+i00000000
χ352-222-2-22-20000−2i2i−2i2i−2i2i−2i2i2-2000000−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i0000002-200−2i2i000000−1+i1−i−1−i1+i00000000
χ362-222-2-22-20000−2i2i−2i2i−2i2i−2i2i2-2000000−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i000000-22002i−2i0000001−i−1+i1+i−1−i00000000
χ372-22-222-2-222-2-2-2-20022000002-200022−2−222−2−222−2−222−2−200002i−2i002i−2i0000000000000000i2−i2i2−i2
χ382-22-222-2-222-2-2-2-20022000002-200022−2−222−2−222−2−222−2−20000−2i2i00−2i2i0000000000000000−i2i2−i2i2
χ392-22-222-2-222-2-2-2-20022000002-2000−2−222−2−222−2−222−2−22200002i−2i002i−2i0000000000000000−i2i2−i2i2
χ402-22-222-2-222-2-2-2-20022000002-2000−2−222−2−222−2−222−2−2220000−2i2i00−2i2i0000000000000000i2−i2i2−i2
χ412-22-222-2-2-2-2222200-2-2000002-2000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002i−2i00−2i2i0000000000000000−222−2
χ422-22-222-2-2-2-2222200-2-2000002-2000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000−2i2i002i−2i00000000000000002−2−22
χ432-22-222-2-2-2-2222200-2-2000002-2000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002i−2i00−2i2i00000000000000002−2−22
χ442-22-222-2-2-2-2222200-2-2000002-2000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−2i2i002i−2i0000000000000000−222−2
χ452-2-2-22-2222-22-2002200-2-2000002-20i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-22-2000000000000000000i2−i2i2−i20000
χ462-2-2-22-2222-22-2002200-2-2000002-20i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-22-22000000000000000000−i2i2−i2i20000
χ472-2-2-22-2222-22-2002200-2-2000002-20−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-22-2000000000000000000−i2i2−i2i20000
χ482-2-2-22-2222-22-2002200-2-2000002-20−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-22-22000000000000000000i2−i2i2−i20000
χ492-2-2-22-222-22-2200-2-20022000002-202−22−22−22−2−22−22−22−222-2-220000000000000000002−2−220000
χ502-2-2-22-222-22-2200-2-20022000002-202−22−22−22−2−22−22−22−22-222-2000000000000000000−222−20000
χ512-2-2-22-222-22-2200-2-20022000002-20−22−22−22−222−22−22−22−22-2-22000000000000000000−222−20000
χ522-2-2-22-222-22-2200-2-20022000002-20−22−22−22−222−22−22−22−2-222-20000000000000000002−2−220000
χ53444-4-4-4-4400004i−4i00−4i4i00000000002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ000000000000000000000000000000
χ54444-4-4-4-4400004i−4i00−4i4i0000000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ000000000000000000000000000000
χ55444-4-4-4-440000−4i4i004i−4i00000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3000000000000000000000000000000
χ56444-4-4-4-440000−4i4i004i−4i0000000000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3000000000000000000000000000000
χ5744-444-4-4-44-4-4400000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ5844-444-4-4-44-4-440000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ5944-444-4-4-4-444-400000000000000002-2-222-2-22-222-2-222-2000000000000000000000000000000
χ6044-444-4-4-4-444-40000000000000000-222-2-222-22-2-222-2-22000000000000000000000000000000
χ6144-4-4-444-40000004i−4i00−4i4i000000002ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000000000
χ6244-4-4-444-40000004i−4i00−4i4i00000000−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ000000000000000000000000000000
χ6344-4-4-444-4000000−4i4i004i−4i000000002ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000
χ6444-4-4-444-4000000−4i4i004i−4i00000000−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000
χ654-444-4-44-400004i−4i−4i4i4i−4i−4i4i-440000000000000000000000000000000000000000000000000000
χ664-444-4-44-40000−4i4i4i−4i−4i4i4i−4i-440000000000000000000000000000000000000000000000000000
χ674-44-444-4-444-4-44400-4-400000-440000000000000000000000000000000000000000000000000
χ684-44-444-4-4-4-444-4-4004400000-440000000000000000000000000000000000000000000000000
χ694-4-44-44-440000000000000040000-42i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ704-4-44-44-440000000000000040000-4−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ714-4-44-44-4400000000000000-4000042-2-22-222-2-222-22-2-22000000000000000000000000000000
χ724-4-44-44-4400000000000000-400004-222-22-2-222-2-22-222-2000000000000000000000000000000
χ734-4-4-44-4444-44-400-4-4004400000-4400000000000000000000000000000000000000000000000
χ744-4-4-44-444-44-44004400-4-400000-4400000000000000000000000000000000000000000000000

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