Finite Group Databasebeta

← Group #310204

Character table — Group #310204

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-11-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-111-1-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-11111-1-1-111-1
χ911111111111111111-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-11111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111111111-1-1-1-11-1-1-1-11
χ17222222222-22-2-222-2-222220000-20000222222-2-2000000-2-20000000000000000000-200000
χ18222222222-22-2-222-2-222220000-20000-2-2-2-2-2-2-2-2000000220000000000000000000200000
χ19222222222-22-2-222-2-2-2-2-2-20000-200002222-2-222000000-2-20000000000000000000200000
χ20222222222-22-2-222-2-2-2-2-2-20000-20000-2-2-2-22222000000220000000000000000000-200000
χ2122222222-22-222-2-22-200002222-2222200000000-2-222-2-200000000000000-2000000000000
χ2222222222-22-222-2-22-200002222-2-2-2-2-200000000-2-2-2-222000000000000002000000000000
χ2322222222-22-222-2-22-20000-2-2-2-2-222220000000022-2-2-2-2000000000000002000000000000
χ2422222222-22-222-2-22-20000-2-2-2-2-2-2-2-2-20000000022222200000000000000-2000000000000
χ2522-2-2-22-2222-2-2-22-2222i2i−2i−2i0000-200000000002i−2i0000000022-2-2000000000002i−2i00000000
χ2622-2-2-22-2222-2-2-22-2222i2i−2i−2i0000-200000000002i−2i00000000-2-22200000000000−2i2i00000000
χ2722-2-2-22-2222-2-2-22-222−2i−2i2i2i0000-20000000000−2i2i0000000022-2-200000000000−2i2i00000000
χ2822-2-2-22-2222-2-2-22-222−2i−2i2i2i0000-20000000000−2i2i00000000-2-222000000000002i−2i00000000
χ2922-2-2-22-222-2-2222-2-2-22i2i−2i−2i2i2i−2i−2i20000000000−2i2i2i−2i00000000000000000002-20000000000
χ3022-2-2-22-222-2-2222-2-2-22i2i−2i−2i−2i−2i2i2i20000000000−2i2i−2i2i0000000000000000000-220000000000
χ3122-2-2-22-222-2-2222-2-2-2−2i−2i2i2i2i2i−2i−2i200000000002i−2i2i−2i0000000000000000000-220000000000
χ3222-2-2-22-222-2-2222-2-2-2−2i−2i2i2i−2i−2i2i2i200000000002i−2i−2i2i00000000000000000002-20000000000
χ3322-2-2-22-22-2-2222-22-2200002i2i−2i−2i-2000000000000−2i2i00000000002i2i−2i−2i0000000002-2000000
χ3422-2-2-22-22-2-2222-22-2200002i2i−2i−2i-2000000000000−2i2i0000000000−2i−2i2i2i000000000-22000000
χ3522-2-2-22-22-2-2222-22-220000−2i−2i2i2i-20000000000002i−2i00000000002i2i−2i−2i000000000-22000000
χ3622-2-2-22-22-2-2222-22-220000−2i−2i2i2i-20000000000002i−2i0000000000−2i−2i2i2i0000000002-2000000
χ372-222-22-2-2-202002-2002i−2i2i−2i00000i2i2−i2−i22i2i−2i−2i2-2000000i2−i20000002−22−222−2−20000000000i2−i20
χ382-222-22-2-2-202002-2002i−2i2i−2i00000i2i2−i2−i2−2i−2i2i2i-22000000i2−i20000002−22−2−2−2220000000000−i2i20
χ392-222-22-2-2-202002-2002i−2i2i−2i00000−i2−i2i2i22i2i−2i−2i2-2000000−i2i2000000−22−22−2−2220000000000−i2i20
χ402-222-22-2-2-202002-2002i−2i2i−2i00000−i2−i2i2i2−2i−2i2i2i-22000000−i2i2000000−22−2222−2−20000000000i2−i20
χ412-222-22-2-2-202002-200−2i2i−2i2i00000i2i2−i2−i22i2i−2i−2i-22000000i2−i2000000−22−2222−2−20000000000−i2i20
χ422-222-22-2-2-202002-200−2i2i−2i2i00000i2i2−i2−i2−2i−2i2i2i2-2000000i2−i2000000−22−22−2−2220000000000i2−i20
χ432-222-22-2-2-202002-200−2i2i−2i2i00000−i2−i2i2i22i2i−2i−2i-22000000−i2i20000002−22−2−2−2220000000000i2−i20
χ442-222-22-2-2-202002-200−2i2i−2i2i00000−i2−i2i2i2−2i−2i2i2i2-2000000−i2i20000002−22−222−2−20000000000−i2i20
χ452-2-222-2-220202-200-2000002i−2i2i−2i02i−2i2i−2i2−22−20000002-2002−2i2−i2i2−i20000i2−i2i2−i2000000002−2000
χ462-2-222-2-220202-200-2000002i−2i2i−2i02i−2i2i−2i−22−220000002-200−22−i2i2−i2i20000−i2i2−i2i200000000−22000
χ472-2-222-2-220202-200-2000002i−2i2i−2i0−2i2i−2i2i2−22−2000000-22002−2i2−i2i2−i20000−i2i2−i2i200000000−22000
χ482-2-222-2-220202-200-2000002i−2i2i−2i0−2i2i−2i2i−22−22000000-2200−22−i2i2−i2i20000i2−i2i2−i2000000002−2000
χ492-2-222-2-220202-200-200000−2i2i−2i2i02i−2i2i−2i2−22−2000000-22002−2−i2i2−i2i20000i2−i2i2−i200000000−22000
χ502-2-222-2-220202-200-200000−2i2i−2i2i02i−2i2i−2i−22−22000000-2200−22i2−i2i2−i20000−i2i2−i2i2000000002−2000
χ512-2-222-2-220202-200-200000−2i2i−2i2i0−2i2i−2i2i2−22−20000002-2002−2−i2i2−i2i20000−i2i2−i2i2000000002−2000
χ522-2-222-2-220202-200-200000−2i2i−2i2i0−2i2i−2i2i−22−220000002-200−22i2−i2i2−i20000i2−i2i2−i200000000−22000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ5444-44-4-44-400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ5544-44-4-44-400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ5644-44-4-44-4000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ5744-44-4-44-4000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ5844-4-4-44-44-444-4-4-444-4000000004000000000000000000000000000000000000000000000
χ594-444-44-4-440-400-44000000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ604-444-44-4-440-400-4400000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ614-44-4-4-444040-4400-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ624-44-4-4-444040-4400-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ634-44-4-4-4440-404-4004000004-4-440000000000000000000000000000000000000000000000
χ644-44-4-4-4440-404-400400000-444-40000000000000000000000000000000000000000000000
χ654-4-444-4-440-40-440040000000000000022−2222−220000000000−22220000000000000000000000000
χ664-4-444-4-440-40-4400400000000000000−2222−2222000000000022−220000000000000000000000000
χ674-4-4-4444-440400-4-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ684-4-4-4444-440400-4-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ694-4-4-4444-4-40-40044004-4-4400000000000000000000000000000000000000000000000000
χ704-4-4-4444-4-40-4004400-444-400000000000000000000000000000000000000000000000000
χ71888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000

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