Finite Group Databasebeta

← Group #310186

Character table — Group #310186

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-111111111-1-1-11-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-11111-1-111-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-1111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111-111-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-222-2-2-22-200002222-22222000000-2-22200-2-200000000000000-2000000000000
χ18222222222-222-2-2-22-200002222-2-2-2-2-2000000-2-2-2-20022000000000000002000000000000
χ19222222222-222-2-2-22-20000-2-2-2-2-2222200000022-2-200-2-2000000000000002000000000000
χ20222222222-222-2-2-22-20000-2-2-2-2-2-2-2-2-20000002222002200000000000000-2000000000000
χ2122222222-22-2-2222-2-222220000-200002222220000-2-200-2-2000000000000000-2000000000
χ2222222222-22-2-2222-2-222220000-20000-2-2-2-2-2-20000-2-200220000000000000002000000000
χ2322222222-22-2-2222-2-2-2-2-2-20000-200002222-2-200002200-2-20000000000000002000000000
χ2422222222-22-2-2222-2-2-2-2-2-20000-20000-2-2-2-2220000220022000000000000000-2000000000
χ2522-2-2-22-2222-2-2-22-2222i2i−2i−2i0000-2000000000000002i−2i000022-2-20000000000002i−2i0000000
χ2622-2-2-22-2222-2-2-22-2222i2i−2i−2i0000-2000000000000002i−2i0000-2-222000000000000−2i2i0000000
χ2722-2-2-22-2222-2-2-22-222−2i−2i2i2i0000-200000000000000−2i2i000022-2-2000000000000−2i2i0000000
χ2822-2-2-22-2222-2-2-22-222−2i−2i2i2i0000-200000000000000−2i2i0000-2-2220000000000002i−2i0000000
χ2922-2-2-22-22-2222-22-2-2-22i2i−2i−2i2i2i−2i−2i200000000002i−2i00−2i2i000000000000000002-20000000000
χ3022-2-2-22-22-2222-22-2-2-22i2i−2i−2i−2i−2i2i2i20000000000−2i2i00−2i2i00000000000000000-220000000000
χ3122-2-2-22-22-2222-22-2-2-2−2i−2i2i2i2i2i−2i−2i200000000002i−2i002i−2i00000000000000000-220000000000
χ3222-2-2-22-22-2222-22-2-2-2−2i−2i2i2i−2i−2i2i2i20000000000−2i2i002i−2i000000000000000002-20000000000
χ3322-2-2-22-22-2-2222-22-2200002i2i−2i−2i-20000000000−2i2i0000000000002i2i−2i−2i00000000002-200000
χ3422-2-2-22-22-2-2222-22-2200002i2i−2i−2i-20000000000−2i2i000000000000−2i−2i2i2i0000000000-2200000
χ3522-2-2-22-22-2-2222-22-220000−2i−2i2i2i-200000000002i−2i0000000000002i2i−2i−2i0000000000-2200000
χ3622-2-2-22-22-2-2222-22-220000−2i−2i2i2i-200000000002i−2i000000000000−2i−2i2i2i00000000002-200000
χ372-22-22-2-220200-2-22002-22-200000i2i2−i2−i222-2-22-2000000i2−i2000000i2−i2i2−i2i2i2−i2−i20000000000i2−i20
χ382-22-22-2-220200-2-22002-22-200000i2i2−i2−i2-2-222-22000000i2−i2000000i2−i2i2−i2−i2−i2i2i20000000000−i2i20
χ392-22-22-2-220200-2-22002-22-200000−i2−i2i2i222-2-22-2000000−i2i2000000−i2i2−i2i2−i2−i2i2i20000000000−i2i20
χ402-22-22-2-220200-2-22002-22-200000−i2−i2i2i2-2-222-22000000−i2i2000000−i2i2−i2i2i2i2−i2−i20000000000i2−i20
χ412-22-22-2-220200-2-2200-22-2200000i2i2−i2−i222-2-2-22000000i2−i2000000−i2i2−i2i2i2i2−i2−i20000000000−i2i20
χ422-22-22-2-220200-2-2200-22-2200000i2i2−i2−i2-2-2222-2000000i2−i2000000−i2i2−i2i2−i2−i2i2i20000000000i2−i20
χ432-22-22-2-220200-2-2200-22-2200000−i2−i2i2i222-2-2-22000000−i2i2000000i2−i2i2−i2−i2−i2i2i20000000000i2−i20
χ442-22-22-2-220200-2-2200-22-2200000−i2−i2i2i2-2-2222-2000000−i2i2000000i2−i2i2−i2i2i2−i2−i20000000000−i2i20
χ452-2-2-2222-2202-2000-2000002-22-202i−2i2i−2i2−22−200002i−2i00002−22−22−20000i2−i2i2−i200000000i2−i2000
χ462-2-2-2222-2202-2000-2000002-22-202i−2i2i−2i−22−2200002i−2i0000−22−22−220000−i2i2−i2i200000000−i2i2000
χ472-2-2-2222-2202-2000-2000002-22-20−2i2i−2i2i2−22−20000−2i2i00002−22−22−20000−i2i2−i2i200000000−i2i2000
χ482-2-2-2222-2202-2000-2000002-22-20−2i2i−2i2i−22−220000−2i2i0000−22−22−220000i2−i2i2−i200000000i2−i2000
χ492-2-2-2222-2202-2000-200000-22-2202i−2i2i−2i2−22−20000−2i2i00002−2−22−220000i2−i2i2−i200000000−i2i2000
χ502-2-2-2222-2202-2000-200000-22-2202i−2i2i−2i−22−220000−2i2i0000−222−22−20000−i2i2−i2i200000000i2−i2000
χ512-2-2-2222-2202-2000-200000-22-220−2i2i−2i2i2−22−200002i−2i00002−2−22−220000−i2i2−i2i200000000i2−i2000
χ522-2-2-2222-2202-2000-200000-22-220−2i2i−2i2i−22−2200002i−2i0000−222−22−20000i2−i2i2−i200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ5444-444-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ5544-444-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ5644-444-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ5744-444-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ5844-4-4-44-444-4-4-44-444-4000000004000000000000000000000000000000000000000000000
χ594-444-44-4-440-44000-400000000000000000000000000000022−22−2222000000000000000000000
χ604-444-44-4-440-44000-4000000000000000000000000000000−222222−22000000000000000000000
χ614-444-44-4-4-404-40004000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ624-444-44-4-4-404-4000400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-44-44-4-440-40044-4000000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ644-44-44-4-440-40044-400000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ654-4-44-4-44404004-4-4004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ664-4-44-4-44404004-4-400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ674-4-44-4-4440-400-4440000000000000000000000000000000000022−22−222200000000000000000
χ684-4-44-4-4440-400-44400000000000000000000000000000000000−222222−2200000000000000000
χ694-4-4-4444-4-40-4400040000000000000022−2222−220000000000−22220000000000000000000000000
χ704-4-4-4444-4-40-44000400000000000000−2222−2222000000000022−220000000000000000000000000
χ71888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000

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