Finite Group Databasebeta

← Group #290237

Character table — Group #290237

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888822444444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111111111-1-1-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-11-111-1-11-1
χ101111111111-1-1-1-111111111-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-1-11-1-111-11
χ111111111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-1111-1-1-111-11
χ121111111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1111-1111-1-11-1
χ131111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1111-1111-1-1-11
χ141111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-11-1111-1-1-1111-1
χ151111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-111-11-1-1-11-1-1111-1
χ161111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111-1-1-11-111-1-1-11
χ17222222222-2222222-2-22-2-2-222-2-2-200000000222200000000-2-2-2-200000000000000
χ18222222222-2222222-2-22-2-2-222-2-2-200000000-2-2-2-200000000222200000000000000
χ19222222222-2-2-2-2-222-2-22-2-2-2-2-22220000000022-2-200000000-2-22200000000000000
χ20222222222-2-2-2-2-222-2-22-2-2-2-2-222200000000-2-2220000000022-2-200000000000000
χ2122222222-222222-2-222-22-2-2-2-222-2000000000000000000000000002-200-22000000
χ2222222222-222222-2-222-22-2-2-2-222-200000000000000000000000000-22002-2000000
χ2322222222-22-2-2-2-2-2-222-22-2-222-2-22000000000000000000000000002200-2-2000000
χ2422222222-22-2-2-2-2-2-222-22-2-222-2-2200000000000000000000000000-2-20022000000
χ2522222222-2-22222-2-2-2-2-2-222-2-2-2-222i2i−2i−2i000000002i2i−2i−2i0000000000000000000000
χ2622222222-2-22222-2-2-2-2-2-222-2-2-2-22−2i−2i2i2i00000000−2i−2i2i2i0000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-22i2i−2i−2i00000000−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2−2i−2i2i2i000000002i2i−2i−2i0000000000000000000000
χ292222-2-2-2-22200002-22-2-2-22-2000002-22-222-2-200000000000000002-2000000000000
χ302222-2-2-2-22200002-22-2-2-22-2000002-22-2-2-2220000000000000000-22000000000000
χ312222-2-2-2-22200002-22-2-2-22-200000-22-2222-2-20000000000000000-22000000000000
χ322222-2-2-2-22200002-22-2-2-22-200000-22-22-2-22200000000000000002-2000000000000
χ332222-2-2-2-2-2-20000-22-22222-2000002i−2i−2i2i00000000000022-2-2000000002i−2i00000000
χ342222-2-2-2-2-2-20000-22-22222-2000002i−2i−2i2i000000000000-2-22200000000−2i2i00000000
χ352222-2-2-2-2-2-20000-22-22222-200000−2i2i2i−2i00000000000022-2-200000000−2i2i00000000
χ362222-2-2-2-2-2-20000-22-22222-200000−2i2i2i−2i000000000000-2-222000000002i−2i00000000
χ3722-2-22-2-222022-2-2-2200-20002-20000000i2−i2i2−i200000000i2−i2i2−i22i−2i2i−2i000000002−22−200
χ3822-2-22-2-222022-2-2-2200-20002-20000000i2−i2i2−i200000000i2−i2i2−i2−2i2i−2i2i00000000−22−2200
χ3922-2-22-2-222022-2-2-2200-20002-20000000−i2i2−i2i200000000−i2i2−i2i22i−2i2i−2i00000000−22−2200
χ4022-2-22-2-222022-2-2-2200-20002-20000000−i2i2−i2i200000000−i2i2−i2i2−2i2i−2i2i000000002−22−200
χ4122-2-22-2-2220-2-222-2200-2000-220000000i2−i2i2−i200000000−i2i2−i2i22i−2i−2i2i000000002−2−2200
χ4222-2-22-2-2220-2-222-2200-2000-220000000i2−i2i2−i200000000−i2i2−i2i2−2i2i2i−2i00000000−222−200
χ4322-2-22-2-2220-2-222-2200-2000-220000000−i2i2−i2i200000000i2−i2i2−i22i−2i−2i2i00000000−222−200
χ4422-2-22-2-2220-2-222-2200-2000-220000000−i2i2−i2i200000000i2−i2i2−i2−2i2i2i−2i000000002−2−2200
χ454444-4-4-4-44-400004-4-44-44-440000000000000000000000000000000000000000000
χ464444-4-4-4-4-440000-444-44-4-440000000000000000000000000000000000000000000
χ4744-4-44-4-44-4044-4-44-4004000-4400000000000000000000000000000000000000000
χ4844-4-44-4-44-40-4-4444-40040004-400000000000000000000000000000000000000000
χ4944-4-4-444-4400000-4-40040000000000002i2−2i2−2i22i2000000000000000000000000000000
χ5044-4-4-444-4400000-4-4004000000000000−2i22i22i2−2i2000000000000000000000000000000
χ5144-4-4-444-4-4000004400-40000000000000000000000002i2−2i2−2i22i2000000000000000000
χ5244-4-4-444-4-4000004400-4000000000000000000000000−2i22i22i2−2i2000000000000000000
χ534-44-444-4-4004i−4i4i−4i00000000000000000000022−222i2−2i200000000000000000000000000
χ544-44-444-4-4004i−4i4i−4i000000000000000000000−2222−2i22i200000000000000000000000000
χ554-44-444-4-400−4i4i−4i4i00000000000000000000022−22−2i22i200000000000000000000000000
χ564-44-444-4-400−4i4i−4i4i000000000000000000000−22222i2−2i200000000000000000000000000
χ574-4-444-44-4044i−4i−4i4i00-4-40400004i−4i000000000000000000000000000000000000000
χ584-4-444-44-404−4i4i4i−4i00-4-4040000−4i4i000000000000000000000000000000000000000
χ594-4-444-44-40-44i−4i−4i4i00440-40000−4i4i000000000000000000000000000000000000000
χ604-4-444-44-40-4−4i4i4i−4i00440-400004i−4i000000000000000000000000000000000000000
χ614-4-44-44-4404000000-440-400000000000000000002i2−2i22i2−2i20000000000000000000000
χ624-4-44-44-4404000000-440-40000000000000000000−2i22i2−2i22i20000000000000000000000
χ634-4-44-44-440-40000004-404000000000000000000022−22−22220000000000000000000000
χ644-4-44-44-440-40000004-4040000000000000000000−222222−220000000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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