Finite Group Databasebeta

← Group #119950

Character table — Group #119950

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444222244442244444444444444444444444444444488888888
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
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ2122222222-2-2-2-22222-2-2-2-22-22-222-2-20000000000000000000000000000000000002i−2i2i−2i
χ2222222222-2-2-2-22222-2-2-2-22-22-222-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-2-2-22222-2-2-2-2-22-22-2-222000000000000000000000000000000002i−2i2i−2i0000
χ2422222222-2-2-2-22222-2-2-2-2-22-22-2-22200000000000000000000000000000000−2i2i−2i2i0000
χ2522222222-2-2-2-2-2-2-2-222222-22-2-2-222000000000000000000000000000000002-2-220000
χ2622222222-2-2-2-2-2-2-2-222222-22-2-2-22200000000000000000000000000000000-222-20000
χ2722222222-2-2-2-2-2-2-2-22222-22-2222-2-20000000000000000000000000000000000002-2-22
χ2822222222-2-2-2-2-2-2-2-22222-22-2222-2-2000000000000000000000000000000000000-222-2
χ2922-22-22-2-22-22-22i2i−2i−2i2i2i−2i−2i00000000002i−2i2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ3022-22-22-2-22-22-22i2i−2i−2i2i2i−2i−2i00000000002i−2i2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ3122-22-22-2-22-22-22i2i−2i−2i2i2i−2i−2i0000000000−2i2i-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ3222-22-22-2-22-22-22i2i−2i−2i2i2i−2i−2i0000000000−2i2i-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ3322-22-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i00000000002i−2i-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ3422-22-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i00000000002i−2i-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ3522-22-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i0000000000−2i2i2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ3622-22-22-2-22-22-2−2i−2i2i2i−2i−2i2i2i0000000000−2i2i2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ372-222-2-22-2-222-22i−2i2i−2i2i−2i2i−2i000000002-200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ382-222-2-22-2-222-22i−2i2i−2i2i−2i2i−2i000000002-200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ392-222-2-22-2-222-22i−2i2i−2i2i−2i2i−2i00000000-220000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ402-222-2-22-2-222-22i−2i2i−2i2i−2i2i−2i00000000-220000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ412-222-2-22-2-222-2−2i2i−2i2i−2i2i−2i2i000000002-20000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ422-222-2-22-2-222-2−2i2i−2i2i−2i2i−2i2i000000002-20000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ432-222-2-22-2-222-2−2i2i−2i2i−2i2i−2i2i00000000-2200002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ442-222-2-22-2-222-2−2i2i−2i2i−2i2i−2i2i00000000-2200002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ452-2-222-2-2222-2-22-2-22-222-22-2-222-22-20000000000000000000000002i−2i2i−2i000000000000
χ462-2-222-2-2222-2-22-2-22-222-22-2-222-22-2000000000000000000000000−2i2i−2i2i000000000000
χ472-2-222-2-2222-2-22-2-22-222-2-222-2-22-2200000000000000000000000000002i−2i2i−2i00000000
χ482-2-222-2-2222-2-22-2-22-222-2-222-2-22-220000000000000000000000000000−2i2i−2i2i00000000
χ492-2-222-2-2222-2-2-222-22-2-222-2-22-22-2200000000000000000000000000002i−2i−2i2i00000000
χ502-2-222-2-2222-2-2-222-22-2-222-2-22-22-220000000000000000000000000000−2i2i2i−2i00000000
χ512-2-222-2-2222-2-2-222-22-2-22-222-22-22-20000000000000000000000002i−2i−2i2i000000000000
χ522-2-222-2-2222-2-2-222-22-2-22-222-22-22-2000000000000000000000000−2i2i2i−2i000000000000
χ532-2-222-2-22-2-2222-2-222-2-2222-2-22-2-2200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ542-2-222-2-22-2-2222-2-222-2-2222-2-22-2-220000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ552-2-222-2-22-2-2222-2-222-2-22-2-222-222-2000000002-2-222-2-22000000000000000000000000
χ562-2-222-2-22-2-2222-2-222-2-22-2-222-222-200000000-222-2-222-2000000000000000000000000
χ572-2-222-2-22-2-222-222-2-222-222-2-2-222-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ582-2-222-2-22-2-222-222-2-222-222-2-2-222-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ592-2-222-2-22-2-222-222-2-222-2-2-2222-2-2200000000000000002-2-222-2-220000000000000000
χ602-2-222-2-22-2-222-222-2-222-2-2-2222-2-220000000000000000-222-2-222-20000000000000000
χ6144-44-44-4-4-44-444i4i−4i−4i−4i−4i4i4i000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-44-44−4i−4i4i4i4i4i−4i−4i000000000000000000000000000000000000000000000000
χ634-444-4-44-44-4-444i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000
χ644-444-4-44-44-4-44−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000
χ65888-88-8-8-8000000000000000000000000000000000000000000000000000000000000
χ6688-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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