Finite Group Databasebeta

← Group #148162

Character table — Group #148162

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order122222222244444444888888888844448888161616161616161616161616161616164444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ9111111-1-1-1-111-1-111-1-1-1-1-1-1111-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ10111111-1-1-1-111-1-111-1-1-1-1-1-1111-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-1-111−i−iii
χ11111111-1-1-1-111-1-111-1-1-1-1-1-1111-11-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-1-111−i−iii
χ12111111-1-1-1-111-1-111-1-1-1-1-1-1111-11-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii11-1-1ii−i−i
χ13111111-1-1-1-111-1-111-1-1-1-1-1-1111-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii
χ14111111-1-1-1-111-1-111-1-1-1-1-1-1111-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−i
χ15111111-1-1-1-111-1-111-1-1-1-1-1-1111-11-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ16111111-1-1-1-111-1-111-1-1-1-1-1-1111-11-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-1-111ii−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
χ19222222-2-2-2-222-2-222-2-22222-2-2-22-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ20222222-2-2-2-222-2-222-2-22222-2-2-22-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ212222-2-222-2-22-22-22-22-222222-2-2-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222222-2-222-2-22-22-22-22-222222-2-2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ232222-2-222-2-22-22-22-22-2-2-2-2-2-2222-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ242222-2-222-2-22-22-22-22-2-2-2-2-2-2222-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ252222-2-2-2-2222-2-222-2-222222-222-2-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ262222-2-2-2-2222-2-222-2-222222-222-2-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ272222-2-2-2-2222-2-222-2-22-2-2-2-22-2-2222000000000000000022-2-2-2-2220000000000000000
χ282222-2-2-2-2222-2-222-2-22-2-2-2-22-2-22220000000000000000-2-22222-2-20000000000000000
χ292-2-222-22-22-2222-2-2-2-2200000000002i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ302-2-222-22-22-2222-2-2-2-2200000000002i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ312-2-222-22-22-2222-2-2-2-220000000000−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ322-2-222-22-22-2222-2-2-2-220000000000−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ332-2-222-22-22-2-2-2-22222-222-2-222-22-2-20000000000000000000000000000000000002i−2i2i−2i
χ342-2-222-22-22-2-2-2-22222-222-2-222-22-2-2000000000000000000000000000000000000−2i2i−2i2i
χ352-2-222-22-22-2-2-2-22222-2-2-222-2-22-222000000000000000000000000000000002-22-20000
χ362-2-222-22-22-2-2-2-22222-2-2-222-2-22-22200000000000000000000000000000000-22-220000
χ372-2-222-2-22-2222-22-2-22-200000000002-2-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ382-2-222-2-22-2222-22-2-22-200000000002-2-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ392-2-222-2-22-2222-22-2-22-20000000000-222-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ402-2-222-2-22-2222-22-2-22-20000000000-222-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ412-2-222-2-22-22-2-22-222-2222-2-2-2-2222-2000000000000000000000000000000002-2-220000
χ422-2-222-2-22-22-2-22-222-2222-2-2-2-2222-200000000000000000000000000000000-222-20000
χ432-2-222-2-22-22-2-22-222-22-2-22222-2-2-220000000000000000000000000000000000002-2-22
χ442-2-222-2-22-22-2-22-222-22-2-22222-2-2-22000000000000000000000000000000000000-222-2
χ452-2-22-222-2-222-222-22-2-2000000000000002i−2i2i−2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ462-2-22-222-2-222-222-22-2-2000000000000002i−2i2i−2i−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ472-2-22-222-2-222-222-22-2-200000000000000−2i2i−2i2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ482-2-22-222-2-222-222-22-2-200000000000000−2i2i−2i2i−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ492-2-22-222-2-22-22-2-22-22222-2-22-22-2-220000000000000000000000002-22-2000000000000
χ502-2-22-222-2-22-22-2-22-22222-2-22-22-2-22000000000000000000000000-22-22000000000000
χ512-2-22-222-2-22-22-2-22-222-2-222-22-222-200000000000000000000000000002-22-200000000
χ522-2-22-222-2-22-22-2-22-222-2-222-22-222-20000000000000000000000000000-22-2200000000
χ532-2-22-22-222-22-2-2-2-2222000000000000002-2-222−2−22−222−22−2−22−222−20000000000000000
χ542-2-22-22-222-22-2-2-2-2222000000000000002-2-22−222−22−2−22−222−22−2−220000000000000000
χ552-2-22-22-222-22-2-2-2-222200000000000000-222-22−2−22−222−2−222−22−2−220000000000000000
χ562-2-22-22-222-22-2-2-2-222200000000000000-222-2−222−22−2−222−2−22−222−20000000000000000
χ572-2-22-22-222-2-22222-2-2-222-2-2-22-2-22200000000000000000000000000002i−2i−2i2i00000000
χ582-2-22-22-222-2-22222-2-2-222-2-2-22-2-2220000000000000000000000000000−2i2i2i−2i00000000
χ592-2-22-22-222-2-22222-2-2-2-2-2222-222-2-20000000000000000000000002-2-22000000000000
χ602-2-22-22-222-2-22222-2-2-2-2-2222-222-2-2000000000000000000000000-222-2000000000000
χ614444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ62444444-4-4-4-4-4-444-4-44400000000000000000000000000000000000000000000000000
χ634444-4-444-4-4-44-44-44-4400000000000000000000000000000000000000000000000000
χ644444-4-4-4-444-444-4-444-400000000000000000000000000000000000000000000000000
χ6588-8-80000000000000042−4242−420000000000000000000000000000000000000000000000
χ6688-8-800000000000000−4242−42420000000000000000000000000000000000000000000000
χ678-88-80000000000000042−42−42420000000000000000000000000000000000000000000000
χ688-88-800000000000000−424242−420000000000000000000000000000000000000000000000

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