Finite Group Databasebeta

← Group #290705

Character table — Group #290705

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888882224444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1111111-1-1-1-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1-1-111111
χ9111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-111-1-1
χ10111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111-1-111
χ11111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11-1-111-1-1111-1-1
χ12111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-111-1-111-1-1-111
χ13111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-111
χ14111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111111-1-1
χ15111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-11-1-111
χ16111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-11111-111-1-1
χ172222222222222222-2-222-2-2-2-22222-2-222-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222222222-2-2-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ2122222222-2-2-2-222222-2-2-222-2-200002-20000000000000000000000002-2-200000020000
χ2222222222-2-2-2-222222-2-2-222-2-200002-2000000000000000000000000-222000000-20000
χ2322222222-2-2-2-22222-22-2-2-2-2220000-220000000000000000000000000002-22-20000000
χ2422222222-2-2-2-22222-22-2-2-2-2220000-22000000000000000000000000000-22-220000000
χ2522222222-2-2-2-2-2-2-2-22-222-2-22200002-20000000000000000000000002-22000000-20000
χ2622222222-2-2-2-2-2-2-2-22-222-2-22200002-2000000000000000000000000-22-200000020000
χ2722222222-2-2-2-2-2-2-2-2-222222-2-20000-220000000000000000000000000002-2-220000000
χ2822222222-2-2-2-2-2-2-2-2-222222-2-20000-22000000000000000000000000000-222-20000000
χ292222-2-2-2-22-22-2000000002i−2i2i−2i22-2-200002i−2i0022−2−2i2i2−i2−i222−2−2i2i2−i2−i20000000000000000
χ302222-2-2-2-22-22-2000000002i−2i2i−2i22-2-200002i−2i00−2−222−i2−i2i2i2−2−222−i2−i2i2i20000000000000000
χ312222-2-2-2-22-22-2000000002i−2i2i−2i-2-2220000−2i2i0022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000000000
χ322222-2-2-2-22-22-2000000002i−2i2i−2i-2-2220000−2i2i00−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000000000
χ332222-2-2-2-22-22-200000000−2i2i−2i2i22-2-20000−2i2i0022−2−2−i2−i2i2i222−2−2−i2−i2i2i20000000000000000
χ342222-2-2-2-22-22-200000000−2i2i−2i2i22-2-20000−2i2i00−2−222i2i2−i2−i2−2−222i2i2−i2−i20000000000000000
χ352222-2-2-2-22-22-200000000−2i2i−2i2i-2-22200002i−2i0022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000000000
χ362222-2-2-2-22-22-200000000−2i2i−2i2i-2-22200002i−2i00−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000000000
χ3722-2-222-2-22-2-2200002-20000002i−2i2i−2i-2200002i−2i00002i−2i2i−2i00002-22-20000000000000000
χ3822-2-222-2-22-2-2200002-20000002i−2i2i−2i-2200002i−2i0000−2i2i−2i2i0000-22-220000000000000000
χ3922-2-222-2-22-2-2200002-2000000−2i2i−2i2i-220000−2i2i00002i−2i2i−2i0000-22-220000000000000000
χ4022-2-222-2-22-2-2200002-2000000−2i2i−2i2i-220000−2i2i0000−2i2i−2i2i00002-22-20000000000000000
χ4122-2-222-2-22-2-220000-220000002i−2i2i−2i2-20000−2i2i2-22-200002i−2i2i−2i00000000000000000000
χ4222-2-222-2-22-2-220000-220000002i−2i2i−2i2-20000−2i2i-22-220000−2i2i−2i2i00000000000000000000
χ4322-2-222-2-22-2-220000-22000000−2i2i−2i2i2-200002i−2i2-22-20000−2i2i−2i2i00000000000000000000
χ4422-2-222-2-22-2-220000-22000000−2i2i−2i2i2-200002i−2i-22-2200002i−2i2i−2i00000000000000000000
χ4522-2-2-2-22222-2-222-2-2002-200002i−2i−2i2i002i−2i00002−2−222−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ4622-2-2-2-22222-2-222-2-2002-200002i−2i−2i2i002i−2i0000−222−2−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ4722-2-2-2-22222-2-222-2-2002-20000−2i2i2i−2i00−2i2i00002−2−222−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ4822-2-2-2-22222-2-222-2-2002-20000−2i2i2i−2i00−2i2i0000−222−2−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ4922-2-2-2-22222-2-2-2-22200-2200002i−2i−2i2i00−2i2i00002−2−22−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ5022-2-2-2-22222-2-2-2-22200-2200002i−2i−2i2i00−2i2i0000−222−22−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ5122-2-2-2-22222-2-2-2-22200-220000−2i2i2i−2i002i−2i00002−2−22−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ5222-2-2-2-22222-2-2-2-22200-220000−2i2i2i−2i002i−2i0000−222−22−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ534444-4-4-4-4-44-44000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ544444-4-4-4-4-44-4400000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5544-4-444-4-4-444-40000440000000000-4-400000000000000000000000000000000000000
χ5644-4-444-4-4-444-40000-4-400000000004400000000000000000000000000000000000000
χ5744-4-4-4-444-4-44444-4-400-44000000000000000000000000000000000000000000000000
χ5844-4-4-4-444-4-444-4-444004-4000000000000000000000000000000000000000000000000
χ594-44-44-44-400004i−4i4i−4i0000000000000000000000000000000000002-200000002i−2i00000
χ604-44-44-44-400004i−4i4i−4i000000000000000000000000000000000000-220000000−2i2i00000
χ614-44-44-44-40000−4i4i−4i4i0000000000000000000000000000000000002-20000000−2i2i00000
χ624-44-44-44-40000−4i4i−4i4i000000000000000000000000000000000000-2200000002i−2i00000
χ634-4-44-444-400004i−4i−4i4i0000000000000000000000000000000000000000000000002i−2i2-2
χ644-4-44-444-400004i−4i−4i4i000000000000000000000000000000000000000000000000−2i2i-22
χ654-4-44-444-40000−4i4i4i−4i0000000000000000000000000000000000000000000000002i−2i-22
χ664-4-44-444-40000−4i4i4i−4i000000000000000000000000000000000000000000000000−2i2i2-2
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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