Finite Group Databasebeta

← Group #148367

Character table — Group #148367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order122222222244444444888888888844448888161616161616161616161616161616162244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91-1-1111-1-11-1111-1-11-1-1-1-111111-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−i11-1-1ii−i−i
χ101-1-1111-1-11-1111-1-11-1-1-1-111111-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−i−iii-1-111−i−iii
χ111-1-1111-1-11-1111-1-11-1-1-1-111111-1-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii1-11-1ii−i−i-1-111−i−iii
χ121-1-1111-1-11-1111-1-11-1-1-1-111111-1-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-11-11−i−iii11-1-1ii−i−i
χ131-1-1111-1-11-1111-1-11-1-1-1-111111-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii11-1-1−i−iii
χ141-1-1111-1-11-1111-1-11-1-1-1-111111-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11ii−i−i-1-111ii−i−i
χ151-1-1111-1-11-1111-1-11-1-1-1-111111-1-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i1-11-1−i−iii-1-111ii−i−i
χ161-1-1111-1-11-1111-1-11-1-1-1-111111-1-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-11-11ii−i−i11-1-1−i−iii
χ17222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ1922222-22-2-2-222-22-2-2-22000000000000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ2022222-22-2-2-222-22-2-2-22000000000000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ2122222-22-2-2-222-22-2-2-2200000000000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ2222222-22-2-2-222-22-2-2-2200000000000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ2322222-22-2-2-2-2-22-2222-222222-2-22-2-20000000000000000000000000000000000002i−2i2i−2i
χ2422222-22-2-2-2-2-22-2222-222222-2-22-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2522222-22-2-2-2-2-22-2222-2-2-2-2-2-222-222000000000000000000000000000000002i−2i2i−2i0000
χ2622222-22-2-2-2-2-22-2222-2-2-2-2-2-222-22200000000000000000000000000000000−2i2i−2i2i0000
χ272222-22-2-2-222-2222-2-2-200000000002-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ282222-22-2-2-222-2222-2-2-200000000002-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ292222-22-2-2-222-2222-2-2-20000000000-22-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ302222-22-2-2-222-2222-2-2-20000000000-22-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ312222-22-2-2-22-22-2-2-22222222-22-2-22-200000000000000000000000000002-22-200000000
χ322222-22-2-2-22-22-2-2-22222222-22-2-22-20000000000000000000000000000-22-2200000000
χ332222-22-2-2-22-22-2-2-2222-2-2-2-22-222-2200000000000000000000000022-2-2000000000000
χ342222-22-2-2-22-22-2-2-2222-2-2-2-22-222-22000000000000000000000000-2-222000000000000
χ352222-2-2-222-22-2-22-222-22222-2-22-2-22000000002-2-222-2-22000000000000000000000000
χ362222-2-2-222-22-2-22-222-22222-2-22-2-2200000000-222-2-222-2000000000000000000000000
χ372222-2-2-222-22-2-22-222-2-2-2-2-222-222-200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ382222-2-2-222-22-2-22-222-2-2-2-2-222-222-20000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ392-2-2222-2-22-2222-2-22-2-222-2-2-2-2-22222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ402-2-2222-2-22-2222-2-22-2-222-2-2-2-2-2222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ412-2-222-2-22-2222-2-22-22-2000000000000002-2-22i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ422-2-222-2-22-2222-2-22-22-2000000000000002-2-22−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ432-2-222-2-22-2222-2-22-22-200000000000000-222-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ442-2-222-2-22-2222-2-22-22-200000000000000-222-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ452-2-222-2-22-22-2-222-22-2222-2-2-2222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ462-2-222-2-22-22-2-222-22-2222-2-2-2222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ472-2-222-2-22-22-2-222-22-22-2-2222-2-2-2220000000000000000000000000000000000002-2-22
χ482-2-222-2-22-22-2-222-22-22-2-2222-2-2-222000000000000000000000000000000000000-222-2
χ492-2-22-2222-2-22-22-2-2-22200000000002i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ502-2-22-2222-2-22-22-2-2-22200000000002i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ512-2-22-2222-2-22-22-2-2-2220000000000−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ522-2-22-2222-2-22-22-2-2-2220000000000−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ532-2-22-2222-2-2-22-2222-2-222-2-22-22-22-20000000000000000000000002-2-22000000000000
χ542-2-22-2222-2-2-22-2222-2-222-2-22-22-22-2000000000000000000000000-222-2000000000000
χ552-2-22-2222-2-2-22-2222-2-2-2-222-22-22-2200000000000000000000000000002i−2i−2i2i00000000
χ562-2-22-2222-2-2-22-2222-2-2-2-222-22-22-220000000000000000000000000000−2i2i2i−2i00000000
χ572-2-22-2-22-2222-2-2-222-2222-2-222-2-2-2200000000000000002-2-22-222-20000000000000000
χ582-2-22-2-22-2222-2-2-222-2222-2-222-2-2-220000000000000000-222-22-2-220000000000000000
χ592-2-22-2-22-2222-2-2-222-22-2-222-2-2222-2000000002-2-22-222-2000000000000000000000000
χ602-2-22-2-22-2222-2-2-222-22-2-222-2-2222-200000000-222-22-2-22000000000000000000000000
χ614444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ624444-4-4-444-4-444-44-4-4400000000000000000000000000000000000000000000000000
χ634-4-4444-4-44-4-4-4-444-44400000000000000000000000000000000000000000000000000
χ644-4-44-4-44-444-4444-4-44-400000000000000000000000000000000000000000000000000
χ6588-8-8000000000000004i2−4i24i2−4i20000000000000000000000000000000000000000000000
χ6688-8-800000000000000−4i24i2−4i24i20000000000000000000000000000000000000000000000
χ678-88-8000000000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ688-88-800000000000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

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