Finite Group Databasebeta

← Group #235598

Character table — Group #235598

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222244444444224444444488888888224444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-1111-1-11-1-1-11111111-1-1-1-111-1-11-11-111-1-111-1-111-1-111-1-1
χ101111-1-1-1-111-1-1111-1-11-1-1-11111111-1-1-1-111-1-11-11-1-1-111-1-111-1-111-1-111
χ111111-1-1-1-111-1-1111-1-11-1-1-11111111-1-1-1-1-1-111-11-1111-1-111-1-1-1-111-1-111
χ121111-1-1-1-111-1-1111-1-11-1-1-11111111-1-1-1-1-1-111-11-11-1-111-1-11111-1-111-1-1
χ131111-1-1-1-111-1-1111-1-11-1-1-1111-1-1-1-111111-1-111-1-1111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-111-1-1111-1-11-1-1-1111-1-1-1-111111-1-111-1-11-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-111-1-1111-1-11-1-1-1111-1-1-1-11111-111-1-111-111-1-1-1-111-1-11111-1-1
χ161111-1-1-1-111-1-1111-1-11-1-1-1111-1-1-1-11111-111-1-111-1-1-11111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-22-2-222-200000000000000002-22-2000000000000
χ18222222222222-2-2-2-2-2-22-2-222-20000000000000000-22-22000000000000
χ1922222222-2-2-2-222222-2-2-2-22-2-200000000000000000000000000002-22-2
χ2022222222-2-2-2-222222-2-2-2-22-2-20000000000000000000000000000-22-22
χ2122222222-2-2-2-2-2-2-2-2-22-2222-2200000000020200-2-20000000000000000
χ2222222222-2-2-2-2-2-2-2-2-22-2222-22000000000-20-200220000000000000000
χ23222222-2-222-2-222-2-22-222-2-2-2222-2-222-2-2000000000000000000000000
χ24222222-2-222-2-222-2-22-222-2-2-22-2-222-2-222000000000000000000000000
χ25222222-2-222-2-2-2-222-222-22-2-2-2000000000000000000002i−2i2i−2i00000000
χ26222222-2-222-2-2-2-222-222-22-2-2-200000000000000000000−2i2i−2i2i00000000
χ27222222-2-2-2-22222-2-222-2-22-22-20000000000000000000000002-22-20000
χ28222222-2-2-2-22222-2-222-2-22-22-2000000000000000000000000-22-220000
χ29222222-2-2-2-222-2-222-2-2-22-2-222000000002020-2-2000000000000000000
χ30222222-2-2-2-222-2-222-2-2-22-2-22200000000-20-2022000000000000000000
χ312222-2-222222222-22-2-2-2-22-2-2222-2-2-2-222000000000000000000000000
χ322222-2-222222222-22-2-2-2-22-2-22-2-22222-2-2000000000000000000000000
χ332222-2-2222222-2-22-222-22-2-2-2-2000000000000000000002i−2i−2i2i00000000
χ342222-2-2222222-2-22-222-22-2-2-2-200000000000000000000−2i2i2i−2i00000000
χ352222-2-222-2-2-2-222-22-2222-2-22-20000000000000000000000002-2-220000
χ362222-2-222-2-2-2-222-22-2222-2-22-2000000000000000000000000-222-20000
χ372222-2-222-2-2-2-2-2-22-22-22-22-2220000000020-20-22000000000000000000
χ382222-2-222-2-2-2-2-2-22-22-22-22-22200000000-20202-2000000000000000000
χ392222-2-2-2-222-2-2-2-2-222-2-22222-200000000000000002-2-22000000000000
χ402222-2-2-2-222-2-2-2-2-222-2-22222-20000000000000000-222-2000000000000
χ412222-2-2-2-2-2-222222-2-2-22222-2-200000000000000000000000000002-2-22
χ422222-2-2-2-2-2-222222-2-2-22222-2-20000000000000000000000000000-222-2
χ432222-2-2-2-2-2-222-2-2-22222-2-22-2200000000020-200-220000000000000000
χ442222-2-2-2-2-2-222-2-2-22222-2-22-22000000000-202002-20000000000000000
χ454-44-4004i−4i4-44i−4i0000000000000022−222i2−2i200000000000000000000000000
χ464-44-4004i−4i4-44i−4i00000000000000−2222−2i22i200000000000000000000000000
χ474-44-4004i−4i-44−4i4i00000000000022−2200002i2−2i2000000000000000000000000
χ484-44-4004i−4i-44−4i4i000000000000−22220000−2i22i2000000000000000000000000
χ494-44-400−4i4i4-4−4i4i0000000000000022−22−2i22i200000000000000000000000000
χ504-44-400−4i4i4-4−4i4i00000000000000−22222i2−2i200000000000000000000000000
χ514-44-400−4i4i-444i−4i00000000000022−220000−2i22i2000000000000000000000000
χ524-44-400−4i4i-444i−4i000000000000−222200002i2−2i2000000000000000000000000
χ5388-8-88-800000000000000000000000000000000000000000000000000
χ5488-8-8-8800000000000000000000000000000000000000000000000000
χ558-8-88000000008i−8i000000000000000000000000000000000000000000
χ568-8-8800000000−8i8i000000000000000000000000000000000000000000

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