Finite Group Databasebeta

← Group #93018

Character table — Group #93018

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222224444444444444444444444444444888888888888883232323232323232
order12222244448888888844444444888816161616161616161616161616161616448888161616161616161688888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ61111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i
χ91111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111iiiiiiii−i−i−i−i−i−i−i−i1-111-1-1iiii−i−i−i−i1-11-1i−ii−i
χ101111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111iiiiiiii−i−i−i−i−i−i−i−i1-111-1-1iiii−i−i−i−i-11-11−ii−ii
χ111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111−i−i−i−i−i−i−i−iiiiiiiii1-111-1-1−i−i−i−iiiii1-11-1−ii−ii
χ121111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111−i−i−i−i−i−i−i−iiiiiiiii1-111-1-1−i−i−i−iiiii-11-11i−ii−i
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111iiiiiiii−i−i−i−i−i−i−i−i-11-1-111−i−i−i−iiiiii−i−ii-111-1
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111iiiiiiii−i−i−i−i−i−i−i−i-11-1-111−i−i−i−iiiii−iii−i1-1-11
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111−i−i−i−i−i−i−i−iiiiiiiii-11-1-111iiii−i−i−i−ii−i−ii1-1-11
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111−i−i−i−i−i−i−i−iiiiiiiii-11-1-111iiii−i−i−i−i−iii−i-111-1
χ17222222222222222222-2-2-2-22-22-2-2-2-2-200000000000000002-2-2-2220000000000000000
χ18222222222222222222-2-2-2-2-22-22-2-2-2-20000000000000000-2222-2-20000000000000000
χ192222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-20000000000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000-2-222220000000000000000
χ21222222-2-2-2-20000000022-2-2222200002222−2−2−2−22222−2−2−2−2-2-2000022−2−222−2−200000000
χ22222222-2-2-2-20000000022-2-222220000−2−2−2−22222−2−2−2−22222-2-20000−2−222−2−22200000000
χ23222222-2-2-2-20000000022-2-2-2-2-2-200002222−2−2−2−22222−2−2−2−2220000−2−222−2−22200000000
χ24222222-2-2-2-20000000022-2-2-2-2-2-20000−2−2−2−22222−2−2−2−2222222000022−2−222−2−200000000
χ25222222-2-2-2-200000000-2-2222-22-20000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-220000i2i2−i2−i2−i2−i2i2i200000000
χ26222222-2-2-2-200000000-2-2222-22-20000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-220000−i2−i2i2i2i2i2−i2−i200000000
χ27222222-2-2-2-200000000-2-222-22-220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22-20000−i2−i2i2i2i2i2−i2−i200000000
χ28222222-2-2-2-200000000-2-222-22-220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22-20000i2i2−i2−i2−i2−i2i2i200000000
χ292-22-22-200002−222−2−22−22-20022-2-222−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ302-22-22-200002−222−2−22−22-20022-2-222−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ312-22-22-200002−222−2−22−22-200-2-22222−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ500−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ322-22-22-200002−222−2−22−22-200-2-22222−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ500−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ332-22-22-200002−222−2−22−2-22002-2-22−2−222ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ500−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ342-22-22-200002−222−2−22−2-22002-2-22−2−222−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ500−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ352-22-22-200002−222−2−22−2-2200-222-2−2−222ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5002−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ362-22-22-200002−222−2−22−2-2200-222-2−2−222−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5002−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ372-22-22-20000−22−2−222−222-20022-2-2−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ700−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ382-22-22-20000−22−2−222−222-20022-2-2−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ700−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ392-22-22-20000−22−2−222−222-200-2-222−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ402-22-22-20000−22−2−222−222-200-2-222−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ412-22-22-20000−22−2−222−22-22002-2-2222−2−2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ422-22-22-20000−22−2−222−22-22002-2-2222−2−2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ432-22-22-20000−22−2−222−22-2200-222-222−2−2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ700−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ442-22-22-20000−22−2−222−22-2200-222-222−2−2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ700−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ454444-4-444-4-400000000000000004i−4i4i−4i00000000000000000000000000000000000000
χ464444-4-444-4-40000000000000000−4i4i−4i4i00000000000000000000000000000000000000
χ474444-4-4-4-44444-4-4-4-44400000000000000000000000000000000000000000000000000
χ484444-4-4-4-444-4-44444-4-400000000000000000000000000000000000000000000000000
χ4944-4-400004-4440000-4-40000000000002-22-22-22-22-22-22-22-20000000000000000000000
χ5044-4-400004-4440000-4-4000000000000-22-22-22-22-22-22-22-220000000000000000000000
χ5144-4-400004-4-4-40000440000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ5244-4-400004-4-4-4000044000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ5344-4-40000-44004i−4i4i−4i000000000000002ζ2−2ζ22ζ2−2ζ2−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ62ζ6−2ζ62ζ6−2ζ60000000000000000000000
χ5444-4-40000-44004i−4i4i−4i00000000000000−2ζ22ζ2−2ζ22ζ22ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ6−2ζ62ζ6−2ζ62ζ60000000000000000000000
χ5544-4-40000-4400−4i4i−4i4i000000000000002ζ6−2ζ62ζ6−2ζ6−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ22ζ2−2ζ22ζ2−2ζ20000000000000000000000
χ5644-4-40000-4400−4i4i−4i4i00000000000000−2ζ62ζ6−2ζ62ζ62ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ2−2ζ22ζ2−2ζ22ζ20000000000000000000000
χ574-44-4-44000022−22−22−22222222−22004i−4i00002i2−2i2−2i22i200000000000000000000000000000000000000
χ584-44-4-44000022−22−22−22222222−2200−4i4i0000−2i22i22i2−2i200000000000000000000000000000000000000
χ594-44-4-440000−22222222−22−22−2222004i−4i0000−2i22i22i2−2i200000000000000000000000000000000000000
χ604-44-4-440000−22222222−22−22−222200−4i4i00002i2−2i2−2i22i200000000000000000000000000000000000000
χ614-4-44004i−4i0022−222i2−2i2−2i22i2−22220000000000002ζ−2ζ−2ζ2ζ−2ζ52ζ52ζ5−2ζ5−2ζ72ζ72ζ7−2ζ72ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ624-4-44004i−4i0022−222i2−2i2−2i22i2−2222000000000000−2ζ2ζ2ζ−2ζ2ζ5−2ζ5−2ζ52ζ52ζ7−2ζ7−2ζ72ζ7−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ634-4-44004i−4i00−2222−2i22i22i2−2i222−220000000000002ζ5−2ζ5−2ζ52ζ52ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ72ζ72ζ7−2ζ70000000000000000000000
χ644-4-44004i−4i00−2222−2i22i22i2−2i222−22000000000000−2ζ52ζ52ζ5−2ζ5−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ7−2ζ7−2ζ72ζ70000000000000000000000
χ654-4-4400−4i4i0022−22−2i22i22i2−2i2−22220000000000002ζ7−2ζ7−2ζ72ζ7−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ5−2ζ5−2ζ52ζ50000000000000000000000
χ664-4-4400−4i4i0022−22−2i22i22i2−2i2−2222000000000000−2ζ72ζ72ζ7−2ζ72ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ52ζ52ζ5−2ζ50000000000000000000000
χ674-4-4400−4i4i00−22222i2−2i2−2i22i222−220000000000002ζ3−2ζ3−2ζ32ζ32ζ7−2ζ7−2ζ72ζ7−2ζ52ζ52ζ5−2ζ5−2ζ2ζ2ζ−2ζ0000000000000000000000
χ684-4-4400−4i4i00−22222i2−2i2−2i22i222−22000000000000−2ζ32ζ32ζ3−2ζ3−2ζ72ζ72ζ7−2ζ72ζ5−2ζ5−2ζ52ζ52ζ−2ζ−2ζ2ζ0000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.