Finite Group Databasebeta

← Group #306366

Character table — Group #306366

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
χ311111111111111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-111-1-11111111111-1-1-1-11111-1-1-11-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-111-1
χ911111111111111111-1-1-1-1111111111111111-1-111-1-111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11111111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-11
χ17222222222-22-22-22-2-222220000-222220000002200-2-2000000-2-200000000000-2000000000
χ18222222222-22-22-22-2-222220000-2-2-2-2-2000000-2-200-2-200000022000000000002000000000
χ19222222222-22-22-22-2-2-2-2-2-20000-22222000000-2-20022000000-2-2000000000002000000000
χ20222222222-22-22-22-2-2-2-2-2-20000-2-2-2-2-20000002200220000002200000000000-2000000000
χ2122222222-22-22-22-22-200002222-2000022222200-2-200-2-200000000000000-2000000000000
χ2222222222-22-22-22-22-200002222-20000-2-2-2-2-2-200-2-20022000000000000002000000000000
χ2322222222-22-22-22-22-20000-2-2-2-2-200002222-2-2002200-2-2000000000000002000000000000
χ2422222222-22-22-22-22-20000-2-2-2-2-20000-2-2-2-2220022002200000000000000-2000000000000
χ2522-2-22-2-22020-20-2020000022-2-20i2i2−i2−i222-2-22-2000000000000i2−i2i2i2−i2−i2i2i2−i2−i200000000i2−i2000
χ2622-2-22-2-22020-20-2020000022-2-20i2i2−i2−i2-2-222-22000000000000i2−i2i2i2−i2−i2−i2−i2i2i200000000−i2i2000
χ2722-2-22-2-22020-20-2020000022-2-20−i2−i2i2i222-2-22-2000000000000−i2i2−i2−i2i2i2−i2−i2i2i200000000−i2i2000
χ2822-2-22-2-22020-20-2020000022-2-20−i2−i2i2i2-2-222-22000000000000−i2i2−i2−i2i2i2i2i2−i2−i200000000i2−i2000
χ2922-2-22-2-22020-20-20200000-2-2220i2i2−i2−i222-2-2-22000000000000i2−i2−i2−i2i2i2i2i2−i2−i200000000−i2i2000
χ3022-2-22-2-22020-20-20200000-2-2220i2i2−i2−i2-2-2222-2000000000000i2−i2−i2−i2i2i2−i2−i2i2i200000000i2−i2000
χ3122-2-22-2-22020-20-20200000-2-2220−i2−i2i2i222-2-2-22000000000000−i2i2i2i2−i2−i2−i2−i2i2i200000000i2−i2000
χ3222-2-22-2-22020-20-20200000-2-2220−i2−i2i2i2-2-2222-2000000000000−i2i2i2i2−i2−i2i2i2−i2−i200000000−i2i2000
χ332-222-2-2-222-2-222-2-22-200002-22-220000000000002-200002i2i−2i−2i00000000000000002i−2i00000
χ342-222-2-2-222-2-222-2-22-200002-22-220000000000002-20000−2i−2i2i2i0000000000000000−2i2i00000
χ352-222-2-2-222-2-222-2-22-20000-22-222000000000000-2200002i2i−2i−2i0000000000000000−2i2i00000
χ362-222-2-2-222-2-222-2-22-20000-22-222000000000000-220000−2i−2i2i2i00000000000000002i−2i00000
χ372-222-2-2-22-222-2-222-2-22i2i−2i−2i00002000000000000002i−2i000000002-22-2000000002i−2i0000000
χ382-222-2-2-22-222-2-222-2-22i2i−2i−2i00002000000000000002i−2i00000000-22-2200000000−2i2i0000000
χ392-222-2-2-22-222-2-222-2-2−2i−2i2i2i0000200000000000000−2i2i000000002-22-200000000−2i2i0000000
χ402-222-2-2-22-222-2-222-2-2−2i−2i2i2i0000200000000000000−2i2i00000000-22-22000000002i−2i0000000
χ412-222-2-2-22-2-222-2-22222i2i−2i−2i2-22-2-2000000000000-22−2i2i000000000000000002i−2i0000000000
χ422-222-2-2-22-2-222-2-22222i2i−2i−2i-22-22-20000000000002-2−2i2i00000000000000000−2i2i0000000000
χ432-222-2-2-22-2-222-2-2222−2i−2i2i2i2-22-2-2000000000000-222i−2i00000000000000000−2i2i0000000000
χ442-222-2-2-22-2-222-2-2222−2i−2i2i2i-22-22-20000000000002-22i−2i000000000000000002i−2i0000000000
χ452-22-222-2-220-20-202002-22-2000002i−2i2i−2ii2−i2i2−i2002i−2i0000i2−i2i2−i2i2−i20000002−22−200000000002−20
χ462-22-222-2-220-20-202002-22-2000002i−2i2i−2i−i2i2−i2i2002i−2i0000−i2i2−i2i2−i2i2000000−22−220000000000−220
χ472-22-222-2-220-20-202002-22-200000−2i2i−2i2ii2−i2i2−i200−2i2i0000i2−i2i2−i2i2−i2000000−22−220000000000−220
χ482-22-222-2-220-20-202002-22-200000−2i2i−2i2i−i2i2−i2i200−2i2i0000−i2i2−i2i2−i2i20000002−22−200000000002−20
χ492-22-222-2-220-20-20200-22-22000002i−2i2i−2ii2−i2i2−i200−2i2i0000i2−i2−i2i2−i2i20000002−22−20000000000−220
χ502-22-222-2-220-20-20200-22-22000002i−2i2i−2i−i2i2−i2i200−2i2i0000−i2i2i2−i2i2−i2000000−22−2200000000002−20
χ512-22-222-2-220-20-20200-22-2200000−2i2i−2i2ii2−i2i2−i2002i−2i0000i2−i2−i2i2−i2i2000000−22−2200000000002−20
χ522-22-222-2-220-20-20200-22-2200000−2i2i−2i2i−i2i2−i2i2002i−2i0000−i2i2i2−i2i2−i20000002−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-44-44040-40-40000000000000000000000000000022−22−222200000000000000000000000
χ55444-4-4-44-44040-40-400000000000000000000000000000−222222−2200000000000000000000000
χ56444-4-4-44-4-40-40404004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ57444-4-4-44-4-40-4040400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ5844-4-44-4-440-404040-400000000002i22i2−2i2−2i2000000000000000000−2i22i2000000000000000000000
χ5944-4-44-4-440-404040-40000000000−2i2−2i22i22i20000000000000000002i2−2i2000000000000000000000
χ604-444-4-4-4444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ614-44-444-4-4-404040-40000000000000002i2−2i22i2−2i200000000−2i22i2000000000000000000000000000
χ624-44-444-4-4-404040-4000000000000000−2i22i2−2i22i2000000002i2−2i2000000000000000000000000000
χ634-4-444-44-400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ644-4-444-44-400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ654-4-444-44-4000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ664-4-444-44-4000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ674-4-4-4-444404040-40-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ684-4-4-4-444404040-40-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ694-4-4-4-44440-40-40404000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-4-44440-40-4040400000-444-40000000000000000000000000000000000000000000000
χ7188-88-88-8-8000000000000000000000000000000000000000000000000000000000000000

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