Finite Group Databasebeta

← Group #305991

Character table — Group #305991

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-11111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-111-1-111-1-11-1
χ911111111111111111-1-1-1-1111111111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111-1111-1-1-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1111-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111111-1-1-11111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11-1-1-111-1-1111-1
χ172222222222-22-2-2-22-22222-200000000-2-2000022-2-22200000000-2-20000000000000000
χ182222222222-22-2-2-22-22222-200000000-2-20000-2-222-2-200000000220000000000000000
χ192222222222-22-2-2-22-2-2-2-2-2-20000000022000022-2-2-2-200000000220000000000000000
χ202222222222-22-2-2-22-2-2-2-2-2-200000000220000-2-2222200000000-2-20000000000000000
χ2122222222-2-22-2222-2-20000-22222-2-2-2-20022-2-2000000000000000000002-20000000000
χ2222222222-2-22-2222-2-20000-22222-2-2-2-200-2-22200000000000000000000-220000000000
χ2322222222-2-22-2222-2-20000-2-2-2-2-2222200222200000000000000000000-2-20000000000
χ2422222222-2-22-2222-2-20000-2-2-2-2-2222200-2-2-2-200000000000000000000220000000000
χ252222-2-2-2-2222-2-22-2-2-222-2-22000000002-2000000000022-2-200000022-2-2000000000000
χ262222-2-2-2-2222-2-22-2-2-222-2-22000000002-20000000000-2-222000000-2-222000000000000
χ272222-2-2-2-2222-2-22-2-2-2-2-222200000000-22000000000022-2-2000000-2-222000000000000
χ282222-2-2-2-2222-2-22-2-2-2-2-222200000000-220000000000-2-22200000022-2-2000000000000
χ292222-2-2-2-222-2-22-22-2222-2-2-222-2-222-2-2-220000000000000022-2-2000000000000000000
χ302222-2-2-2-222-2-22-22-2222-2-2-2-2-222-2-222-2200000000000000-2-222000000000000000000
χ312222-2-2-2-222-2-22-22-22-2-222-222-2-222-2-22-200000000000000-2-222000000000000000000
χ322222-2-2-2-222-2-22-22-22-2-222-2-2-222-2-2222-20000000000000022-2-2000000000000000000
χ332222-2-2-2-2-2-2-222-222-20000222-2-2-2-22200000000000000000000000000002i−2i2i−2i000000
χ342222-2-2-2-2-2-2-222-222-20000222-2-2-2-2220000000000000000000000000000−2i2i−2i2i000000
χ352222-2-2-2-2-2-2-222-222-200002-2-22222-2-200000000000000000000000000002i−2i−2i2i000000
χ362222-2-2-2-2-2-2-222-222-200002-2-22222-2-20000000000000000000000000000−2i2i2i−2i000000
χ3722-2-222-2-22-20-2000202i−2i2i−2i02−22−22−22−2000000002i−2i00i2−i2i2−i2i2−i2i2−i22-22−22−2000000000000
χ3822-2-222-2-22-20-2000202i−2i2i−2i02−22−22−22−200000000−2i2i00−i2i2−i2i2i2−i2i2−i2-22−22−22000000000000
χ3922-2-222-2-22-20-2000202i−2i2i−2i0−22−22−22−22000000002i−2i00−i2i2−i2i2−i2i2−i2i22-2−22−22000000000000
χ4022-2-222-2-22-20-2000202i−2i2i−2i0−22−22−22−2200000000−2i2i00i2−i2i2−i2−i2i2−i2i2-222−22−2000000000000
χ4122-2-222-2-22-20-200020−2i2i−2i2i02−22−22−22−2000000002i−2i00i2−i2i2−i2−i2i2−i2i2-22−22−22000000000000
χ4222-2-222-2-22-20-200020−2i2i−2i2i02−22−22−22−200000000−2i2i00−i2i2−i2i2−i2i2−i2i22-22−22−2000000000000
χ4322-2-222-2-22-20-200020−2i2i−2i2i0−22−22−22−22000000002i−2i00−i2i2−i2i2i2−i2i2−i2-222−22−2000000000000
χ4422-2-222-2-22-20-200020−2i2i−2i2i0−22−22−22−2200000000−2i2i00i2−i2i2−i2i2−i2i2−i22-2−22−22000000000000
χ4522-2-2-2-2222-202000-202i−2i−2i2i02−2−222−2−220000002i−2i002-2i2−i2−i2i2i2−i2−i2i2002−2−22000000000000
χ4622-2-2-2-2222-202000-202i−2i−2i2i02−2−222−2−22000000−2i2i00-22−i2i2i2−i2i2−i2−i2i200−222−2000000000000
χ4722-2-2-2-2222-202000-202i−2i−2i2i0−222−2−222−20000002i−2i002-2−i2i2i2−i2−i2i2i2−i200−222−2000000000000
χ4822-2-2-2-2222-202000-202i−2i−2i2i0−222−2−222−2000000−2i2i00-22i2−i2−i2i2−i2i2i2−i2002−2−22000000000000
χ4922-2-2-2-2222-202000-20−2i2i2i−2i02−2−222−2−220000002i−2i00-22i2−i2−i2i2−i2i2i2−i200−222−2000000000000
χ5022-2-2-2-2222-202000-20−2i2i2i−2i02−2−222−2−22000000−2i2i002-2−i2i2i2−i2−i2i2i2−i2002−2−22000000000000
χ5122-2-2-2-2222-202000-20−2i2i2i−2i0−222−2−222−20000002i−2i00-22−i2i2i2−i2i2−i2−i2i2002−2−22000000000000
χ5222-2-2-2-2222-202000-20−2i2i2i−2i0−222−2−222−2000000−2i2i002-2i2−i2−i2i2i2−i2−i2i200−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-444-44-4440000-40000000000000000000000000000000000000000000000
χ5544-4-444-4-4-4404000-400000022−2222−22−2222−222200000000000000000000000000000000000000
χ5644-4-444-4-4-4404000-4000000−2222−222222−2222−2200000000000000000000000000000000000000
χ5744-4-4-4-444-440-4000400000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-4-4-4-444-440-40004000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-4-444-4-4400404-4-400000000000000000004i−4i00000000000000000000000000000000
χ604-4-444-4-4400404-4-40000000000000000000−4i4i00000000000000000000000000000000
χ614-4-444-4-4400-40-444000000000000000000000000000000000000000000000000022−2200
χ624-4-444-4-4400-40-4440000000000000000000000000000000000000000000000000−222200
χ634-4-44-444-40040-4-44000000000000000000000000000000000000000000000002i2−2i20000
χ644-4-44-444-40040-4-4400000000000000000000000000000000000000000000000−2i22i20000
χ654-4-44-444-400-4044-4000000000000000004i−4i0000000000000000000000000000000000
χ664-4-44-444-400-4044-400000000000000000−4i4i0000000000000000000000000000000000
χ678-88-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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