Finite Group Databasebeta

← Group #148778

Character table — Group #148778

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order122222222244444444888888888844448888161616161616161616161616161616164444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ91-11-1111-1-1-111-1-1-11-1111-1-1111-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−iii−i−i11-1-111-1-1
χ101-11-1111-1-1-111-1-1-11-1111-1-1111-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii−i−iii-1-111-1-111
χ111-11-1111-1-1-111-1-1-11-1111-1-1111-1-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111
χ121-11-1111-1-1-111-1-1-11-1111-1-1111-1-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1
χ131-11-1111-1-1-111-1-1-11-1111-1-1111-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111
χ141-11-1111-1-1-111-1-1-11-1111-1-1111-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1
χ151-11-1111-1-1-111-1-1-11-1111-1-1111-1-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−iii−i−i−i−iii-1-11111-1-1
χ161-11-1111-1-1-111-1-1-11-1111-1-1111-1-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111
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
χ1922222-2-22-2-2222-2-2-22-200000000002i−2i2i−2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ2022222-2-22-2-2222-2-2-22-200000000002i−2i2i−2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000
χ2122222-2-22-2-2222-2-2-22-20000000000−2i2i−2i2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ2222222-2-22-2-2222-2-2-22-20000000000−2i2i−2i2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000
χ2322222-2-22-2-2-2-2-2222-2222222-2-22-2-20000000000000000000000000000000000002-22-2
χ2422222-2-22-2-2-2-2-2222-2222222-2-22-2-2000000000000000000000000000000000000-22-22
χ2522222-2-22-2-2-2-2-2222-22-2-2-2-2-222-22200000000000000000000000000002i−2i2i−2i00000000
χ2622222-2-22-2-2-2-2-2222-22-2-2-2-2-222-2220000000000000000000000000000−2i2i−2i2i00000000
χ272222-22-2-22-22-222-22-2-22222-22-2-22-2000000000000000000000000000000002i−2i2i−2i0000
χ282222-22-2-22-22-222-22-2-22222-22-2-22-200000000000000000000000000000000−2i2i−2i2i0000
χ292222-22-2-22-22-222-22-2-2-2-2-2-22-222-220000000000000000000000002-22-2000000000000
χ302222-22-2-22-22-222-22-2-2-2-2-2-22-222-22000000000000000000000000-22-22000000000000
χ312222-22-2-22-2-22-2-22-222000000000000002-22-22−22−22−22−22−22−22−22−20000000000000000
χ322222-22-2-22-2-22-2-22-222000000000000002-22-2−22−22−22−22−22−22−22−220000000000000000
χ332222-22-2-22-2-22-2-22-22200000000000000-22-222−22−22−22−2−22−22−22−220000000000000000
χ342222-22-2-22-2-22-2-22-22200000000000000-22-22−22−22−22−222−22−22−22−20000000000000000
χ352222-2-22-2-22-22-22-222-22222-2-22-2-22000000002-2-222-2-22000000000000000000000000
χ362222-2-22-2-22-22-22-222-22222-2-22-2-2200000000-222-2-222-2000000000000000000000000
χ372222-2-22-2-22-22-22-222-2-2-2-2-222-222-200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ382222-2-22-2-22-22-22-222-2-2-2-2-222-222-20000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ392-22-2222-2-2-222-2-2-22-22-2-222-2-2-22222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ402-22-2222-2-2-222-2-2-22-22-2-222-2-2-2222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ412-22-22-2-2-22222-222-2-2-200000000002-2-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ422-22-22-2-2-22222-222-2-2-200000000002-2-220000−2−22222−2−2−2−22222−2−20000000000000000
χ432-22-22-2-2-22222-222-2-2-20000000000-222-2000022−2−2−2−222−2−22222−2−20000000000000000
χ442-22-22-2-2-22222-222-2-2-20000000000-222-20000−2−22222−2−222−2−2−2−2220000000000000000
χ452-22-22-2-2-222-2-22-2-222222-2-22-2-2-2220000000000000000000000000000000000002-2-22
χ462-22-22-2-2-222-2-22-2-222222-2-22-2-2-222000000000000000000000000000000000000-222-2
χ472-22-22-2-2-222-2-22-2-2222-2-222-2222-2-200000000000000000000000000002-2-2200000000
χ482-22-22-2-2-222-2-22-2-2222-2-222-2222-2-20000000000000000000000000000-222-200000000
χ492-22-2-22-22-222-2-2-2222-222-2-2-22-22-22000000000000000000000000000000002i−2i−2i2i0000
χ502-22-2-22-22-222-2-2-2222-222-2-2-22-22-2200000000000000000000000000000000−2i2i2i−2i0000
χ512-22-2-22-22-222-2-2-2222-2-2-2222-22-22-20000000000000000000000002i−2i−2i2i000000000000
χ522-22-2-22-22-222-2-2-2222-2-2-2222-22-22-2000000000000000000000000−2i2i2i−2i000000000000
χ532-22-2-22-22-22-2222-2-2-22000000000000002i−2i−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ542-22-2-22-22-22-2222-2-2-22000000000000002i−2i−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ552-22-2-22-22-22-2222-2-2-2200000000000000−2i2i2i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ562-22-2-22-22-22-2222-2-2-2200000000000000−2i2i2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ572-22-2-2-2222-2-222-222-2-222-2-2-2-2222-2000000002-2-22-222-2000000000000000000000000
χ582-22-2-2-2222-2-222-222-2-222-2-2-2-2222-200000000-222-22-2-22000000000000000000000000
χ592-22-2-2-2222-2-222-222-2-2-2-22222-2-2-2200000000000000002-2-22-222-20000000000000000
χ602-22-2-2-2222-2-222-222-2-2-2-22222-2-2-220000000000000000-222-22-2-220000000000000000
χ614444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ624444-4-44-4-444-44-44-4-4400000000000000000000000000000000000000000000000000
χ634-44-4444-4-4-4-4-4444-44-400000000000000000000000000000000000000000000000000
χ644-44-4-4-4444-44-4-44-4-44400000000000000000000000000000000000000000000000000
χ6588-8-80000000000000042−4242−420000000000000000000000000000000000000000000000
χ6688-8-800000000000000−4242−42420000000000000000000000000000000000000000000000
χ678-8-880000000000000042−42−42420000000000000000000000000000000000000000000000
χ688-8-8800000000000000−424242−420000000000000000000000000000000000000000000000

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