Finite Group Databasebeta

← Group #284090

Character table — Group #284090

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888224444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1111-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-111-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-11-1-1111-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-11-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-1-111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-1-111-1-11-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1111-1-1-1-1-111-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-111111-1-11-1
χ17222222222-2-22-222-2-22222-2000000002200-2-2-2-200-2-222000000000000000000000000
χ18222222222-2-22-222-2-22222-200000000-2-200-2-2220022-2-2000000000000000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-200000000220022-2-20022-2-2000000000000000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-200000000-2-200222200-2-222000000000000000000000000
χ2122222222-222-22-2-22-20000-22222-2-2-2-20022000022000000000000000000-200-2000000
χ2222222222-222-22-2-22-20000-22222-2-2-2-200-2-20000-2-20000000000000000002002000000
χ2322222222-222-22-2-22-20000-2-2-2-2-2222200220000-2-2000000000000000000-2002000000
χ2422222222-222-22-2-22-20000-2-2-2-2-2222200-2-2000022000000000000000000200-2000000
χ252222-2-2-2-2-200202-2002i2i−2i−2i0i2i2−i2−i2i2i2−i2−i22-200000000002i−2i22−2−2i2i2−i2−i222−2−2000000000000
χ262222-2-2-2-2-200202-2002i2i−2i−2i0i2i2−i2−i2i2i2−i2−i2-220000000000−2i2i22−2−2−i2−i2i2i2−2−222000000000000
χ272222-2-2-2-2-200202-2002i2i−2i−2i0−i2−i2i2i2−i2−i2i2i22-200000000002i−2i−2−222−i2−i2i2i2−2−222000000000000
χ282222-2-2-2-2-200202-2002i2i−2i−2i0−i2−i2i2i2−i2−i2i2i2-220000000000−2i2i−2−222i2i2−i2−i222−2−2000000000000
χ292222-2-2-2-2-200202-200−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i22-20000000000−2i2i−2−222i2i2−i2−i2−2−222000000000000
χ302222-2-2-2-2-200202-200−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i2-2200000000002i−2i−2−222−i2−i2i2i222−2−2000000000000
χ312222-2-2-2-2-200202-200−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i22-20000000000−2i2i22−2−2−i2−i2i2i222−2−2000000000000
χ322222-2-2-2-2-200202-200−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i2-2200000000002i−2i22−2−2i2i2−i2−i2−2−222000000000000
χ332-2-2222-2-220020-2-2002i−2i2i−2i02−22−22−22−20000002i−2i002-200i2−i2i2−i2i2−i2i2−i22−22−2000000000000
χ342-2-2222-2-220020-2-2002i−2i2i−2i02−22−22−22−2000000−2i2i00-2200i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ352-2-2222-2-220020-2-2002i−2i2i−2i0−22−22−22−220000002i−2i002-200−i2i2−i2i2−i2i2−i2i2−22−22000000000000
χ362-2-2222-2-220020-2-2002i−2i2i−2i0−22−22−22−22000000−2i2i00-2200−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ372-2-2222-2-220020-2-200−2i2i−2i2i02−22−22−22−20000002i−2i00-2200−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ382-2-2222-2-220020-2-200−2i2i−2i2i02−22−22−22−2000000−2i2i002-200−i2i2−i2i2−i2i2−i2i22−22−2000000000000
χ392-2-2222-2-220020-2-200−2i2i−2i2i0−22−22−22−220000002i−2i00-2200i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ402-2-2222-2-220020-2-200−2i2i−2i2i0−22−22−22−22000000−2i2i002-200i2−i2i2−i2i2−i2i2−i2−22−22000000000000
χ412-2-22-2-222222-2-22-2-2-2000022i−2i−2i2i−2i2i2i−2i000000000000000000000000002-202i−2i0000000
χ422-2-22-2-222222-2-22-2-2-2000022i−2i−2i2i−2i2i2i−2i00000000000000000000000000-220−2i2i0000000
χ432-2-22-2-222222-2-22-2-2-200002−2i2i2i−2i2i−2i−2i2i000000000000000000000000002-20−2i2i0000000
χ442-2-22-2-222222-2-22-2-2-200002−2i2i2i−2i2i−2i−2i2i00000000000000000000000000-2202i−2i0000000
χ452-2-22-2-222-2222-2-22-222-2-22-22i−2i−2i2i2i−2i−2i2i00002-200000000−2i2i2i−2i00000000000000000000
χ462-2-22-2-222-2222-2-22-222-2-22-2−2i2i2i−2i−2i2i2i−2i00002-2000000002i−2i−2i2i00000000000000000000
χ472-2-22-2-222-2222-2-22-22-222-2-22i−2i−2i2i2i−2i−2i2i0000-22000000002i−2i−2i2i00000000000000000000
χ482-2-22-2-222-2222-2-22-22-222-2-2−2i2i2i−2i−2i2i2i−2i0000-2200000000−2i2i2i−2i00000000000000000000
χ492-2-22-2-222-2-2-222-222-22-2-222000000000000-220000000000002-2-222-2-22000000000000
χ502-2-22-2-222-2-2-222-222-22-2-222000000000000-22000000000000-222-2-222-2000000000000
χ512-2-22-2-222-2-2-222-222-2-222-220000000000002-20000000000002-2-22-222-2000000000000
χ522-2-22-2-222-2-2-222-222-2-222-220000000000002-2000000000000-222-22-2-22000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ544444-4-4-4-4400-40-4400000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ554444-4-4-4-4400-40-440000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-4-44-44-404-40400-40000000000000000000000000000000000000000000000002i2−2i200
χ5744-4-44-44-404-40400-4000000000000000000000000000000000000000000000000−2i22i200
χ5844-4-44-44-40-440-400400000000000000004-40000000000000000000000000000000000
χ5944-4-44-44-40-440-40040000000000000000-440000000000000000000000000000000000
χ604-44-4-444-404-40-4004000000000000000000000000000000000000000000000022−220000
χ614-44-4-444-404-40-40040000000000000000000000000000000000000000000000−22220000
χ624-44-4-444-40-440400-400000000000000000000004i−4i0000000000000000000000000000
χ634-44-4-444-40-440400-40000000000000000000000−4i4i0000000000000000000000000000
χ644-4-4444-4-4-400-4044000000022−2222−22−2222−222200000000000000000000000000000000000000
χ654-4-4444-4-4-400-40440000000−2222−222222−2222−2200000000000000000000000000000000000000
χ664-4-44-4-4444-4-4-444-4440000-40000000000000000000000000000000000000000000000
χ6788-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-88-88-8-88000000000000000000000000000000000000000000000000000000000000

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