Finite Group Databasebeta

← Group #350194

Character table — Group #350194

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442244444444444444222244444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-111-1-11111111111-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-111111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ172222222222-2-222-2-22222-2-200000000-2-2000022-2-2-2000000-2-20022000000000000000000
χ182222222222-2-222-2-22222-2-200000000-2-20000-2-222-20000002200-2-2000000000000000000
χ192222222222-2-222-2-2-2-2-2-22200000000-2-2000022222000000-2-200-2-2000000000000000000
χ202222222222-2-222-2-2-2-2-2-22200000000-2-20000-2-2-2-22000000220022000000000000000000
χ2122222222-2-222-2-22222-2-2-2-22222-2-2-2-2-2-200000000222000000-2-200000000000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-2000000002-2-20000002200000000000000000000
χ2322222222-2-222-2-222-2-2222222222222-2-200000000-2-2-2000000-2-200000000000000000000
χ2422222222-2-222-2-222-2-22222-2-2-2-2-2-2-2-2-2-200000000-2220000002200000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222000000002222-2-20000-20022-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2220000000022-2-2220000-200-2-222000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2000000002222-2-20000200-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-20000000022-2-222000020022-2-2000000000000000000000000
χ2922-2-222-2-2002-2002-2002i−2i2i−2i22-2-22i2i−2i−2i0000000000000000000000022−2−2i2i2−i2−i22−2i2−i2000000
χ3022-2-222-2-2002-2002-2002i−2i2i−2i22-2-22i2i−2i−2i00000000000000000000000−2−222−i2−i2i2i2−22−i2i2000000
χ3122-2-222-2-2002-2002-2002i−2i2i−2i-2-222−2i−2i2i2i0000000000000000000000022−2−2i2i2−i2−i2−22−i2i2000000
χ3222-2-222-2-2002-2002-2002i−2i2i−2i-2-222−2i−2i2i2i00000000000000000000000−2−222−i2−i2i2i22−2i2−i2000000
χ3322-2-222-2-2002-2002-200−2i2i−2i2i22-2-2−2i−2i2i2i0000000000000000000000022−2−2−i2−i2i2i22−2−i2i2000000
χ3422-2-222-2-2002-2002-200−2i2i−2i2i22-2-2−2i−2i2i2i00000000000000000000000−2−222i2i2−i2−i2−22i2−i2000000
χ3522-2-222-2-2002-2002-200−2i2i−2i2i-2-2222i2i−2i−2i0000000000000000000000022−2−2−i2−i2i2i2−22i2−i2000000
χ3622-2-222-2-2002-2002-200−2i2i−2i2i-2-2222i2i−2i−2i00000000000000000000000−2−222i2i2−i2−i22−2−i2i2000000
χ372-22-22-22-22-22-22-2-220000002i−2i2i−2i00002-20000002i−2i0002-22-2002i−2i2i−2i000000000000000000
χ382-22-22-22-22-22-22-2-220000002i−2i2i−2i00002-2000000−2i2i000-22-22002i−2i−2i2i000000000000000000
χ392-22-22-22-22-22-22-2-22000000−2i2i−2i2i00002-20000002i−2i000-22-2200−2i2i2i−2i000000000000000000
χ402-22-22-22-22-22-22-2-22000000−2i2i−2i2i00002-2000000−2i2i0002-22-200−2i2i−2i2i000000000000000000
χ412-22-22-22-22-2-222-22-200000000002i−2i2i−2i-222-22-2002i−2i02i−2i00000000−2i2i000000000000000000
χ422-22-22-22-22-2-222-22-200000000002i−2i2i−2i-22-22-2200−2i2i02i−2i000000002i−2i000000000000000000
χ432-22-22-22-22-2-222-22-20000000000−2i2i−2i2i-222-22-200−2i2i0−2i2i000000002i−2i000000000000000000
χ442-22-22-22-22-2-222-22-20000000000−2i2i−2i2i-22-22-22002i−2i0−2i2i00000000−2i2i000000000000000000
χ452-22-22-22-2-222-2-22-220000002i−2i2i−2i0000-222-2-222i−2i0000000002i−2i−2i2i00000000000000000000
χ462-22-22-22-2-222-2-22-220000002i−2i2i−2i0000-22-222-2−2i2i000000000−2i2i−2i2i00000000000000000000
χ472-22-22-22-2-222-2-22-22000000−2i2i−2i2i0000-222-2-22−2i2i000000000−2i2i2i−2i00000000000000000000
χ482-22-22-22-2-222-2-22-22000000−2i2i−2i2i0000-22-222-22i−2i0000000002i−2i2i−2i00000000000000000000
χ492-22-22-22-2-22-22-222-200000000002i−2i2i−2i2-200002i−2i000−2i2i2-2-22−2i2i0000000000000000000000
χ502-22-22-22-2-22-22-222-200000000002i−2i2i−2i2-20000−2i2i000−2i2i-222-22i−2i0000000000000000000000
χ512-22-22-22-2-22-22-222-20000000000−2i2i−2i2i2-200002i−2i0002i−2i-222-2−2i2i0000000000000000000000
χ522-22-22-22-2-22-22-222-20000000000−2i2i−2i2i2-20000−2i2i0002i−2i2-2-222i−2i0000000000000000000000
χ534444-4-4-4-44-400-440000000000000000000000000000000000000000000000000000022−2200
χ544444-4-4-4-44-400-4400000000000000000000000000000000000000000000000000000−222200
χ554444-4-4-4-4-44004-400000000000000000000000000000000000000000000000000022−220000
χ564444-4-4-4-4-44004-4000000000000000000000000000000000000000000000000000−22220000
χ5744-4-444-4-400-4400-44004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ5844-4-444-4-400-4400-4400−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ594-44-4-44-444400-4-40000000000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ604-44-4-44-444400-4-4000000000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ614-44-4-44-44-4-40044000000000000000000000000000000000000000000022−2222−220000000000
χ624-44-4-44-44-4-400440000000000000000000000000000000000000000000−2222−22220000000000
χ634-4-444-4-44004400-4-40000004i−4i−4i4i000000000000000000000000000000000000000000000
χ644-4-444-4-44004400-4-4000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ654-4-444-4-4400-4-4004400000000004-4-4400000000000000000000000000000000000000000
χ664-4-444-4-4400-4-400440000000000-444-400000000000000000000000000000000000000000
χ674-4-44-444-4000000004-4000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ684-4-44-444-4000000004-400000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ694-4-44-444-400000000-44000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ704-4-44-444-400000000-4400000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ7188-8-8-8-888000000000000000000000000000000000000000000000000000000000000000

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