Finite Group Databasebeta

← Group #97502

Character table — Group #97502

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444444444448888888888888888222244444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
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
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-111-1-11-11-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111-1-1111-1-11-11ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1-1-111-111-1-11−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-11111-1-1-11-111-1−i−iii−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-111-1-11-11-11-1−i−iii−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111-1-1111-1-11-11−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1-1-111-111-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-11111-1-1-11-111-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-222-222-2-2-2-2-2-200000000000000000000000022220000-2-2000000000000
χ1822222222222222-2-2-222-222-2-2-2-2-2-2000000000000000000000000-2-2-2-2000022000000000000
χ1922222222222-2-2-22222-22-2-222-2-2-2-2000000000000000000002222000000-2-200000000000000
χ2022222222222-2-2-22222-22-2-222-2-2-2-200000000000000000000-2-2-2-20000002200000000000000
χ2122222222222-2-2-2-2-2-22-2-2-2-2-2-22222000000000000000022-2-200000000-220000000000000000
χ2222222222222-2-2-2-2-2-22-2-2-2-2-2-222220000000000000000-2-222000000002-20000000000000000
χ2322222222-2-2-2222222-222-2-2-2-222-2-20000000000000000222200000000-2-20000000000000000
χ2422222222-2-2-2222222-222-2-2-2-222-2-20000000000000000-2-2-2-200000000220000000000000000
χ2522222222-2-2-2222-2-2-2-22-2-2-222-2-2220000000000000000000022-2-2000000-2200000000000000
χ2622222222-2-2-2222-2-2-2-22-2-2-222-2-22200000000000000000000-2-2220000002-200000000000000
χ2722222222-2-2-2-2-2-2222-2-2222-2-2-2-22200000000000000000000000022-2-20000-22000000000000
χ2822222222-2-2-2-2-2-2222-2-2222-2-2-2-222000000000000000000000000-2-22200002-2000000000000
χ2922-2-222-2-222-20002-2-2-202002-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200002i−2i2i−2i000000000000002−22−20000
χ3022-2-222-2-222-20002-2-2-202002-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000−2i2i−2i2i00000000000000−22−220000
χ3122-2-222-2-222-20002-2-2-202002-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200002i−2i2i−2i00000000000000−22−220000
χ3222-2-222-2-222-20002-2-2-202002-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000−2i2i−2i2i000000000000002−22−20000
χ3322-2-222-2-2-2-22000-22220-2002-200002222−2−2−2−2−2−2−2−2222200002i−2i−2i2i00000000000000−i2i2i2−i20000
χ3422-2-222-2-2-2-22000-22220-2002-200002222−2−2−2−2−2−2−2−222220000−2i2i2i−2i00000000000000i2−i2−i2i20000
χ3522-2-222-2-2-2-22000-22220-2002-20000−2−2−2−222222222−2−2−2−200002i−2i−2i2i00000000000000i2−i2−i2i20000
χ3622-2-222-2-2-2-22000-22220-2002-20000−2−2−2−222222222−2−2−2−20000−2i2i2i−2i00000000000000−i2i2i2−i20000
χ372-22-22-22-22-222-2-2000-2202-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000002i−2i2i−2i000000000000002−22−2
χ382-22-22-22-22-222-2-2000-2202-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000−2i2i−2i2i00000000000000−22−22
χ392-22-22-22-22-222-2-2000-2202-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000002i−2i2i−2i00000000000000−22−22
χ402-22-22-22-22-222-2-2000-2202-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000−2i2i−2i2i000000000000002−22−2
χ412-22-22-22-2-22-2-2220002-202-200000022−2−222−2−2−2−222−2−222000000002i−2i−2i2i00000000000000−i2i2i2−i2
χ422-22-22-22-2-22-2-2220002-202-200000022−2−222−2−2−2−222−2−22200000000−2i2i2i−2i00000000000000i2−i2−i2i2
χ432-22-22-22-2-22-2-2220002-202-2000000−2−222−2−22222−2−222−2−2000000002i−2i−2i2i00000000000000i2−i2−i2i2
χ442-22-22-22-2-22-2-2220002-202-2000000−2−222−2−22222−2−222−2−200000000−2i2i2i−2i00000000000000−i2i2i2−i2
χ452-2-2-2-222200022-222-20-2-200002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-22-200000000000000i2−i2i2−i200000000
χ462-2-2-2-222200022-222-20-2-200002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-22-2200000000000000−i2i2−i2i200000000
χ472-2-2-2-222200022-222-20-2-200002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-22-200000000000000−i2i2−i2i200000000
χ482-2-2-2-222200022-222-20-2-200002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-22-2200000000000000i2−i2i2−i200000000
χ492-2-2-2-2222000-2-22-2-2202200002-2002−22−22−22−2−22−22−22−222-2-22000000000000002−2−2200000000
χ502-2-2-2-2222000-2-22-2-2202200002-2002−22−22−22−2−22−22−22−22-222-200000000000000−222−200000000
χ512-2-2-2-2222000-2-22-2-2202200002-200−22−22−22−222−22−22−22−22-2-2200000000000000−222−200000000
χ522-2-2-2-2222000-2-22-2-2202200002-200−22−22−22−222−22−22−22−2-222-2000000000000002−2−2200000000
χ53444-4-4-4-440000000000000000004i−4i2ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ54444-4-4-4-440000000000000000004i−4i−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ55444-4-4-4-44000000000000000000−4i4i2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ56444-4-4-4-44000000000000000000−4i4i−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ5744-44-4-44-40004-440000-40000000002-2-222-2-222-2-222-2-22000000000000000000000000000000
χ5844-44-4-44-40004-440000-4000000000-222-2-222-2-222-2-222-2000000000000000000000000000000
χ5944-44-4-44-4000-44-4000040000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ6044-44-4-44-4000-44-400004000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ6144-4-444-4-444-4000-444-40-400-4400000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-4-440004-4-440400-4400000000000000000000000000000000000000000000000000
χ634-444-44-4-40000004-4400-4000000002-22-2-22-222-22-2-22-22000000000000000000000000000000
χ644-444-44-4-40000004-4400-400000000-22-222-22-2-22-222-22-2000000000000000000000000000000
χ654-444-44-4-4000000-44-4004000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ664-444-44-4-4000000-44-400400000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ674-44-44-44-44-44-444000-4-40-440000000000000000000000000000000000000000000000000000
χ684-44-44-44-4-44-44-4-4000440-440000000000000000000000000000000000000000000000000000
χ694-4-444-4-444-4-40000004000000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000
χ704-4-444-4-444-4-400000040000000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000
χ714-4-444-4-44-444000000-400000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ724-4-444-4-44-444000000-40000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ734-4-4-4-444400044-4-4-440-440000-44000000000000000000000000000000000000000000000000
χ744-4-4-4-4444000-4-4444-404-40000-44000000000000000000000000000000000000000000000000

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