Finite Group Databasebeta

← Group #306352

Character table — Group #306352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-11-1-1111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-11111-11-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1111111111111-1-1-1-1-1-1-1-11
χ17222222222-22-22-22-2-200002222-22222000000-2-20022000000-2-2000000000-200000000000
χ18222222222-22-22-22-2-200002222-2-2-2-2-2000000-2-200-2-200000022000000000200000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-222220000002200-2-2000000-2-2000000000200000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-2-2-200000022002200000022000000000-200000000000
χ2122222222-22-22-22-22-222220000-2000022222200-2-200-2-200000000000000-2000000000000
χ2222222222-22-22-22-22-222220000-20000-2-2-2-2-2-200-2-20022000000000000002000000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-200002222-2-2002200-2-2000000000000002000000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-20000-2-2-2-2220022002200000000000000-2000000000000
χ252-222-22-2-22-2-222-2-22-222-2-2000020000000000002-200002i2i−2i−2i00000000000000002i−2i00000
χ262-222-22-2-22-2-222-2-22-222-2-2000020000000000002-20000−2i−2i2i2i0000000000000000−2i2i00000
χ272-222-22-2-22-2-222-2-22-2-2-22200002000000000000-2200002i2i−2i−2i0000000000000000−2i2i00000
χ282-222-22-2-22-2-222-2-22-2-2-22200002000000000000-220000−2i−2i2i2i00000000000000002i−2i00000
χ292-222-22-2-2-222-2-222-2-200002i2i−2i−2i200000000002i−2i00000000000022-2-2000000002i−2i0000000
χ302-222-22-2-2-222-2-222-2-200002i2i−2i−2i200000000002i−2i000000000000-2-22200000000−2i2i0000000
χ312-222-22-2-2-222-2-222-2-20000−2i−2i2i2i20000000000−2i2i00000000000022-2-200000000−2i2i0000000
χ322-222-22-2-2-222-2-222-2-20000−2i−2i2i2i20000000000−2i2i000000000000-2-222000000002i−2i0000000
χ332-222-22-2-2-2-222-2-222222-2-22i2i−2i−2i-20000000000−2i2i-22000000000000000000002i−2i000000000
χ342-222-22-2-2-2-222-2-222222-2-2−2i−2i2i2i-200000000002i−2i-2200000000000000000000−2i2i000000000
χ352-222-22-2-2-2-222-2-2222-2-2222i2i−2i−2i-20000000000−2i2i2-200000000000000000000−2i2i000000000
χ362-222-22-2-2-2-222-2-2222-2-222−2i−2i2i2i-200000000002i−2i2-2000000000000000000002i−2i000000000
χ372-22-22-22-2-202020-20000002i−2i2i−2i022-2-2i2i2−i2−i20000002i−2ii2−i22−22−2000000i2i2−i2−i200000000002−20
χ382-22-22-22-2-202020-20000002i−2i2i−2i022-2-2−i2−i2i2i20000002i−2i−i2i2−22−22000000−i2−i2i2i20000000000−220
χ392-22-22-22-2-202020-20000002i−2i2i−2i0-2-222i2i2−i2−i2000000−2i2ii2−i22−22−2000000−i2−i2i2i20000000000−220
χ402-22-22-22-2-202020-20000002i−2i2i−2i0-2-222−i2−i2i2i2000000−2i2i−i2i2−22−22000000i2i2−i2−i200000000002−20
χ412-22-22-22-2-202020-2000000−2i2i−2i2i022-2-2i2i2−i2−i2000000−2i2ii2−i2−22−22000000i2i2−i2−i20000000000−220
χ422-22-22-22-2-202020-2000000−2i2i−2i2i022-2-2−i2−i2i2i2000000−2i2i−i2i22−22−2000000−i2−i2i2i200000000002−20
χ432-22-22-22-2-202020-2000000−2i2i−2i2i0-2-222i2i2−i2−i20000002i−2ii2−i2−22−22000000−i2−i2i2i200000000002−20
χ442-22-22-22-2-202020-2000000−2i2i−2i2i0-2-222−i2−i2i2i20000002i−2i−i2i22−22−2000000i2i2−i2−i20000000000−220
χ452-2-2-222-2202020-20-202i−2i2i−2i000002−22−22i−2i2i−2i2-20000000000002−2i2−i2i2−i2i2−i2i2−i2000000002−2000
χ462-2-2-222-2202020-20-202i−2i2i−2i000002−22−2−2i2i−2i2i-220000000000002−2i2−i2i2−i2−i2i2−i2i200000000−22000
χ472-2-2-222-2202020-20-202i−2i2i−2i00000−22−222i−2i2i−2i2-2000000000000−22−i2i2−i2i2−i2i2−i2i200000000−22000
χ482-2-2-222-2202020-20-202i−2i2i−2i00000−22−22−2i2i−2i2i-22000000000000−22−i2i2−i2i2i2−i2i2−i2000000002−2000
χ492-2-2-222-2202020-20-20−2i2i−2i2i000002−22−22i−2i2i−2i-220000000000002−2−i2i2−i2i2i2−i2i2−i200000000−22000
χ502-2-2-222-2202020-20-20−2i2i−2i2i000002−22−2−2i2i−2i2i2-20000000000002−2−i2i2−i2i2−i2i2−i2i2000000002−2000
χ512-2-2-222-2202020-20-20−2i2i−2i2i00000−22−222i−2i2i−2i-22000000000000−22i2−i2i2−i2−i2i2−i2i2000000002−2000
χ522-2-2-222-2202020-20-20−2i2i−2i2i00000−22−22−2i2i−2i2i2-2000000000000−22i2−i2i2−i2i2−i2i2−i200000000−22000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-4-444040-40-40000004-4-440000000000000000000000000000000000000000000000
χ55444-4-4-4-444040-40-4000000-444-40000000000000000000000000000000000000000000000
χ56444-4-4-4-44-40-40404000000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ57444-4-4-4-44-40-4040400000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ5844-444-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ5944-444-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ6044-444-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ6144-444-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ6244-4-4-444-4040-40-40400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ6344-4-4-444-4040-40-4040000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6444-4-4-444-40-404040-404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6544-4-4-444-40-404040-40−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ664-444-44-4-444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ674-44-44-44-440-40-4040000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ684-44-44-44-440-40-404000000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ694-4-4-444-440-40-40404000000000022−2222−22000000000000000000−2222000000000000000000000
χ704-4-4-444-440-40-404040000000000−2222−222200000000000000000022−22000000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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