Finite Group Databasebeta

← Group #306713

Character table — Group #306713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888244444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-11-1-111-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1111
χ51111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-11111-1
χ911111111111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11-1-111-1-11-1-111-1-11
χ1011111111111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1111111-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-11111-1-1111-1-1-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1111111-1-111-1-1-1-1-111-1-1-1-1-1-1-111111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111-1-1-1-1111-1-1-1-1111
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-11111-11111-1-1-1
χ17222222222-22-22-22-2-20000-22222220000-2-222000000-2-2000000-200000000000000
χ18222222222-22-22-22-2-20000-22222-2-2000022-2-2000000-2-2000000200000000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-2220000-2-2-2-200000022000000200000000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-20000222200000022000000-200000000000000
χ2122222222-22-22-22-22-22222-2000000-2-2220000-2-20000002200000000000-20000000
χ2222222222-22-22-22-22-22222-2000000-2-2-2-2000022000000-2-20000000000020000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000002222000022000000-2-200000000000-20000000
χ2422222222-22-22-22-22-2-2-2-2-2-200000022-2-20000-2-2000000220000000000020000000
χ25222-2-2-2-222-2-222-2-22-22i2i−2i−2i20000002i−2i000000000000000000000002i−2i00000002-20
χ26222-2-2-2-222-2-222-2-22-22i2i−2i−2i20000002i−2i00000000000000000000000−2i2i0000000-220
χ27222-2-2-2-222-2-222-2-22-2−2i−2i2i2i2000000−2i2i000000000000000000000002i−2i0000000-220
χ28222-2-2-2-222-2-222-2-22-2−2i−2i2i2i2000000−2i2i00000000000000000000000−2i2i00000002-20
χ29222-2-2-2-22-222-2-222-2-20000200002-200002-200002i2i−2i−2i0000000002i−2i000000000000
χ30222-2-2-2-22-222-2-222-2-20000200002-200002-20000−2i−2i2i2i000000000−2i2i000000000000
χ31222-2-2-2-22-222-2-222-2-2000020000-220000-2200002i2i−2i−2i000000000−2i2i000000000000
χ32222-2-2-2-22-222-2-222-2-2000020000-220000-220000−2i−2i2i2i0000000002i−2i000000000000
χ33222-2-2-2-22-2-222-2-22222i2i−2i−2i-200002-2−2i2i00-220000000000000000000002i−2i00000000
χ34222-2-2-2-22-2-222-2-22222i2i−2i−2i-20000-22−2i2i002-2000000000000000000000−2i2i00000000
χ35222-2-2-2-22-2-222-2-2222−2i−2i2i2i-200002-22i−2i00-22000000000000000000000−2i2i00000000
χ36222-2-2-2-22-2-222-2-2222−2i−2i2i2i-20000-222i−2i002-20000000000000000000002i−2i00000000
χ372-2-222-2-2202020-20-202i−2i2i−2i022−2−200002-2000000i2−i2i2−i22−22i−2ii2i2−i2−i200000000002−2000
χ382-2-222-2-2202020-20-202i−2i2i−2i022−2−20000-22000000i2−i2i2−i22−2−2i2i−i2−i2i2i20000000000−22000
χ392-2-222-2-2202020-20-202i−2i2i−2i0−2−22200002-2000000−i2i2−i2i2−222i−2i−i2−i2i2i20000000000−22000
χ402-2-222-2-2202020-20-202i−2i2i−2i0−2−2220000-22000000−i2i2−i2i2−22−2i2ii2i2−i2−i200000000002−2000
χ412-2-222-2-2202020-20-20−2i2i−2i2i022−2−200002-2000000−i2i2−i2i22−2−2i2i−i2−i2i2i200000000002−2000
χ422-2-222-2-2202020-20-20−2i2i−2i2i022−2−20000-22000000−i2i2−i2i22−22i−2ii2i2−i2−i20000000000−22000
χ432-2-222-2-2202020-20-20−2i2i−2i2i0−2−22200002-2000000i2−i2i2−i2−22−2i2ii2i2−i2−i20000000000−22000
χ442-2-222-2-2202020-20-20−2i2i−2i2i0−2−2220000-22000000i2−i2i2−i2−222i−2i−i2−i2i2i200000000002−2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-4444-4-444-4-440000-40000000000000000000000000000000000000000000
χ4744-44-44-4-44040-40-4000000000000000000000000000000022−2222−22000000000000000
χ4844-44-44-4-44040-40-40000000000000000000000000000000−2222−2222000000000000000
χ4944-44-44-4-4-40-4040400000004i−4i4i−4i000000000000000000000000000000000000000
χ5044-44-44-4-4-40-404040000000−4i4i−4i4i000000000000000000000000000000000000000
χ5144-4-44-44-440-40-40400000000000000000004i−4i00000000000000000000000000000
χ5244-4-44-44-440-40-4040000000000000000000−4i4i00000000000000000000000000000
χ5344-4-44-44-4-404040-400000000000000000000000000000000000000000002i2−2i200000
χ5444-4-44-44-4-404040-40000000000000000000000000000000000000000000−2i22i200000
χ554-444-4-44-4000000000000002i2−2i2−2i22i2000000000022−22000000002i−2i−2i2i000000000000000
χ564-444-4-44-4000000000000002i2−2i2−2i22i20000000000−222200000000−2i2i2i−2i000000000000000
χ574-444-4-44-400000000000000−2i22i22i2−2i2000000000022−2200000000−2i2i2i−2i000000000000000
χ584-444-4-44-400000000000000−2i22i22i2−2i20000000000−2222000000002i−2i−2i2i000000000000000
χ594-4-444-4-440-40-404040000002222−22−220000000000000000−2222000000000000000000000
χ604-4-444-4-440-40-40404000000−22−222222000000000000000022−22000000000000000000000
χ614-4-4-4-4444040-40-404000000000000000000000022−22−222200000000000000000000000
χ624-4-4-4-4444040-40-4040000000000000000000000−222222−2200000000000000000000000
χ634-4-4-4-44440-404040-404-4-4400000000000000000000000000000000000000000000
χ644-4-4-4-44440-404040-40-444-400000000000000000000000000000000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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