Finite Group Databasebeta

← Group #149173

Character table — Group #149173

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order122222222222444444448888888844448888161616161616161616161616161616164444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-1111-1-11-1-1111-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1111-1-11-1-1111-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1111-1-11-1-1111-1-1-11-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−i
χ1211111111-1-1-1-1111-1-11-1-1111-1-1-11-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iii
χ1311111111-1-1-1-1111-1-11-1-1111-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1411111111-1-1-1-1111-1-11-1-1111-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1511111111-1-1-1-1111-1-11-1-1111-1-1-11-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii
χ1611111111-1-1-1-1111-1-11-1-1111-1-1-11-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i
χ1722222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ1922222222-2-2-2-2222-2-22-2-2-2-2-2222-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ2022222222-2-2-2-2222-2-22-2-2-2-2-2222-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ21222-22-2-2-22-22-222-222-2-2-2000000002-22-2000022−2−222−2−222−2−222−2−20000000000000000
χ22222-22-2-2-22-22-222-222-2-2-2000000002-22-20000−2−222−2−222−2−222−2−2220000000000000000
χ23222-22-2-2-22-22-222-222-2-2-200000000-22-22000022−2−222−2−2−2−222−2−2220000000000000000
χ24222-22-2-2-22-22-222-222-2-2-200000000-22-220000−2−222−2−22222−2−222−2−20000000000000000
χ25222-22-2-2-22-22-2-2-22-2-222222-22-2-2-22000000000000000000000000000000002i−2i2i−2i0000
χ26222-22-2-2-22-22-2-2-22-2-222222-22-2-2-2200000000000000000000000000000000−2i2i−2i2i0000
χ27222-22-2-2-22-22-2-2-22-2-2222-2-22-2222-200000000000000000000000000002i−2i2i−2i00000000
χ28222-22-2-2-22-22-2-2-22-2-2222-2-22-2222-20000000000000000000000000000−2i2i−2i2i00000000
χ29222-22-2-2-2-22-2222-2-2-2-222000000002i−2i−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ30222-22-2-2-2-22-2222-2-2-2-222000000002i−2i−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ31222-22-2-2-2-22-2222-2-2-2-22200000000−2i2i2i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ32222-22-2-2-2-22-2222-2-2-2-22200000000−2i2i2i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ33222-22-2-2-2-22-22-2-22222-2-222-2-222-2-2000000000000000000000000000000002-2-220000
χ34222-22-2-2-2-22-22-2-22222-2-222-2-222-2-200000000000000000000000000000000-222-20000
χ35222-22-2-2-2-22-22-2-22222-2-2-2-222-2-22200000000000000000000000000002i−2i−2i2i00000000
χ36222-22-2-2-2-22-22-2-22222-2-2-2-222-2-2220000000000000000000000000000−2i2i2i−2i00000000
χ372-2-222-2-222-2-222-222-2-22-20000000000002-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-222-2-222-2-222-222-2-22-20000000000002-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-222-2-222-2-222-222-2-22-2000000000000-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-2-222-2-222-2-222-222-2-22-2000000000000-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-2-222-2-222-2-22-22-2-222-222-2222-2-2-20000000000000000000000002i−2i2i−2i000000000000
χ422-2-222-2-222-2-22-22-2-222-222-2222-2-2-2000000000000000000000000−2i2i−2i2i000000000000
χ432-2-222-2-222-2-22-22-2-222-22-22-2-2-22220000000000000000000000000000000000002-22-2
χ442-2-222-2-222-2-22-22-2-222-22-22-2-2-2222000000000000000000000000000000000000-22-22
χ452-2-222-2-22-222-22-22-22-2-220000000000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ462-2-222-2-22-222-22-22-22-2-220000000000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ472-2-222-2-22-222-22-22-22-2-22000000000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ482-2-222-2-22-222-22-22-22-2-22000000000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ492-2-222-2-22-222-2-22-22-222-22-22-2-22-220000000000000000000000002i−2i−2i2i000000000000
χ502-2-222-2-22-222-2-22-22-222-22-22-2-22-22000000000000000000000000−2i2i2i−2i000000000000
χ512-2-222-2-22-222-2-22-22-222-2-22-222-22-20000000000000000000000000000000000002i−2i−2i2i
χ522-2-222-2-22-222-2-22-22-222-2-22-222-22-2000000000000000000000000000000000000−2i2i2i−2i
χ532-2-2-2222-222-2-22-2-22-22-222-2-22-222-200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ542-2-2-2222-222-2-22-2-22-22-222-2-22-222-20000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ552-2-2-2222-222-2-22-2-22-22-22-222-22-2-22000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ562-2-2-2222-222-2-22-2-22-22-22-222-22-2-2200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ572-2-2-2222-2-2-2222-2-2-2222-22-2-2-22-22200000000000000002-2-22-222-20000000000000000
χ582-2-2-2222-2-2-2222-2-2-2222-22-2-2-22-2220000000000000000-222-22-2-220000000000000000
χ592-2-2-2222-2-2-2222-2-2-2222-2-2222-22-2-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ602-2-2-2222-2-2-2222-2-2-2222-2-2222-22-2-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ61444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ6244444444-4-4-4-4-4-4-444-444000000000000000000000000000000000000000000000000
χ634-4-4-4444-444-4-4-444-44-44-4000000000000000000000000000000000000000000000000
χ644-4-4-4444-4-4-444-4444-4-4-44000000000000000000000000000000000000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ6688-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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