Finite Group Databasebeta

← Group #308117

Character table — Group #308117

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11-1-111-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111-1-1111-1-1-1-1-1-11
χ172222222222-2-2-222-20000-22222-20000222200-2-20022000000-2-20000000000000-20000000
χ182222222222-2-2-222-20000-22222-20000-2-2-2-200-2-200-2-200000022000000000000020000000
χ192222222222-2-2-222-20000-2-2-2-2-2-200002222002200-2-2000000-2-2000000000000020000000
χ202222222222-2-2-222-20000-2-2-2-2-2-20000-2-2-2-200220022000000220000000000000-20000000
χ2122222222-2-2222-2-222222-20000-222220000-2-20022000000-2-20000000000-2000000000000
χ2222222222-2-2222-2-222222-20000-2-2-2-2-20000-2-200-2-20000002200000000002000000000000
χ2322222222-2-2222-2-22-2-2-2-2-20000-2222200002200-2-2000000-2-200000000002000000000000
χ2422222222-2-2222-2-22-2-2-2-2-20000-2-2-2-2-20000220022000000220000000000-2000000000000
χ2522-22-22-2-2222-22-2-2-222-2-220000-2000000002-200000022-2-200000000000002-20000000000
χ2622-22-22-2-2222-22-2-2-222-2-220000-2000000002-2000000-2-2220000000000000-220000000000
χ2722-22-22-2-2222-22-2-2-2-2-22220000-200000000-2200000022-2-20000000000000-220000000000
χ2822-22-22-2-2222-22-2-2-2-2-22220000-200000000-22000000-2-22200000000000002-20000000000
χ2922-22-22-2-2-2-22-2222-222-2-2-22i2i−2i−2i200000000-222i−2i000000000000000000000002i−2i00000000
χ3022-22-22-2-2-2-22-2222-222-2-2-2−2i−2i2i2i200000000-22−2i2i00000000000000000000000−2i2i00000000
χ3122-22-22-2-2-2-22-2222-2-2-222-22i2i−2i−2i2000000002-22i−2i00000000000000000000000−2i2i00000000
χ3222-22-22-2-2-2-22-2222-2-2-222-2−2i−2i2i2i2000000002-2−2i2i000000000000000000000002i−2i00000000
χ3322-22-22-2-2-2-2-22-2222000022i2i−2i−2i-20000000000−2i2i00000000000022-2-200000000002i−2i00000
χ3422-22-22-2-2-2-2-22-2222000022i2i−2i−2i-20000000000−2i2i000000000000-2-2220000000000−2i2i00000
χ3522-22-22-2-2-2-2-22-222200002−2i−2i2i2i-200000000002i−2i00000000000022-2-20000000000−2i2i00000
χ3622-22-22-2-2-2-2-22-222200002−2i−2i2i2i-200000000002i−2i000000000000-2-22200000000002i−2i00000
χ372-22-222-2-200-2-220022-22-20000002i2i−2i−2i22−2−200002i−2i000000002−22−22−2i2i2−i2−i200000000i2−i2000
χ382-22-222-2-200-2-220022-22-20000002i2i−2i−2i−2−22200002i−2i00000000−22−22−22−i2−i2i2i200000000−i2i2000
χ392-22-222-2-200-2-220022-22-2000000−2i−2i2i2i22−2−20000−2i2i000000002−22−22−2−i2−i2i2i200000000−i2i2000
χ402-22-222-2-200-2-220022-22-2000000−2i−2i2i2i−2−2220000−2i2i00000000−22−22−22i2i2−i2−i200000000i2−i2000
χ412-22-222-2-200-2-22002-22-220000002i2i−2i−2i22−2−20000−2i2i000000002−2−22−22i2i2−i2−i200000000−i2i2000
χ422-22-222-2-200-2-22002-22-220000002i2i−2i−2i−2−2220000−2i2i00000000−222−22−2−i2−i2i2i200000000i2−i2000
χ432-22-222-2-200-2-22002-22-22000000−2i−2i2i2i22−2−200002i−2i000000002−2−22−22−i2−i2i2i200000000i2−i2000
χ442-22-222-2-200-2-22002-22-22000000−2i−2i2i2i−2−22200002i−2i00000000−222−22−2i2i2−i2−i200000000−i2i2000
χ452-2-222-22-22-20002-20000002-22-20i2−i2i2−i22i−2i2i−2i0000002i−2ii2−i2i2−i2i2−i20000002−22−200000000002−20
χ462-2-222-22-22-20002-20000002-22-20i2−i2i2−i2−2i2i−2i2i000000−2i2ii2−i2i2−i2i2−i2000000−22−220000000000−220
χ472-2-222-22-22-20002-20000002-22-20−i2i2−i2i22i−2i2i−2i0000002i−2i−i2i2−i2i2−i2i2000000−22−220000000000−220
χ482-2-222-22-22-20002-20000002-22-20−i2i2−i2i2−2i2i−2i2i000000−2i2i−i2i2−i2i2−i2i20000002−22−200000000002−20
χ492-2-222-22-22-20002-2000000-22-220i2−i2i2−i22i−2i2i−2i000000−2i2i−i2i2−i2i2i2−i20000002−22−20000000000−220
χ502-2-222-22-22-20002-2000000-22-220i2−i2i2−i2−2i2i−2i2i0000002i−2i−i2i2−i2i2i2−i2000000−22−2200000000002−20
χ512-2-222-22-22-20002-2000000-22-220−i2i2−i2i22i−2i2i−2i000000−2i2ii2−i2i2−i2−i2i2000000−22−2200000000002−20
χ522-2-222-22-22-20002-2000000-22-220−i2i2−i2i2−2i2i−2i2i0000002i−2ii2−i2i2−i2−i2i20000002−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ5444-44-44-4-444-44-4-4-440000-400004000000000000000000000000000000000000000000000
χ5544-4-44-4-4400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ5644-4-44-4-4400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ5744-4-44-4-44000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ5844-4-44-4-44000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ594-444-4-4-444-4000-440000000000000000000000000002i2−2i2−2i22i20000000000000000000000000
χ604-444-4-4-444-4000-44000000000000000000000000000−2i22i22i2−2i20000000000000000000000000
χ614-444-4-4-44-440004-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ624-444-4-4-44-440004-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-44-444-4-40044-400-4000000000000002222−22−2200000000000000−2222000000000000000000000
χ644-44-444-4-40044-400-400000000000000−22−2222220000000000000022−22000000000000000000000
χ654-4-444-44-4-44000-44000000000002i2−2i22i2−2i20000000000000000−2i22i200000000000000000000000
χ664-4-444-44-4-44000-4400000000000−2i22i2−2i22i200000000000000002i2−2i200000000000000000000000
χ674-4-4-4-4444004-4-4004000000000000000000000000000000000022−22−222200000000000000000
χ684-4-4-4-4444004-4-40040000000000000000000000000000000000−222222−2200000000000000000
χ694-4-4-4-444400-44400-44-4-44000000000000000000000000000000000000000000000000000
χ704-4-4-4-444400-44400-4-444-4000000000000000000000000000000000000000000000000000
χ71888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000

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