Finite Group Databasebeta

← Group #312313

Character table — Group #312313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-111-111-1-11-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-11-1-1-1-1-1-1-111-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-1111
χ51111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-111111
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-1-1-1111-1-1-1-11-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111111-1-1-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ1011111111111111111-1-1-1-111111-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11111-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111111-1-111-1-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1111-1-1111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-111111-1-11111-1
χ17222222222-22-22-22-2-20000-222220022-2-2-2-200-2-2000000000000000000020000000
χ18222222222-22-22-22-2-20000-2222200-2-2222200-2-20000000000000000000-20000000
χ19222222222-22-22-22-2-20000-2-2-2-2-2002222-2-200220000000000000000000-20000000
χ20222222222-22-22-22-2-20000-2-2-2-2-200-2-2-2-2220022000000000000000000020000000
χ2122222222-22-22-22-22-22222-20000-2-20000002200-2-2000022000000-2000000000000
χ2222222222-22-22-22-22-22222-20000-2-2000000-2-200220000-2-20000002000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000220000002200220000-2-2000000-2000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000022000000-2-200-2-20000220000002000000000000
χ25222-2-2-22-22-2-222-2-22-22i2i−2i−2i200002i−2i0000000000000000000000000002-202i−2i00000
χ26222-2-2-22-22-2-222-2-22-22i2i−2i−2i200002i−2i000000000000000000000000000-220−2i2i00000
χ27222-2-2-22-22-2-222-2-22-2−2i−2i2i2i20000−2i2i0000000000000000000000000002-20−2i2i00000
χ28222-2-2-22-22-2-222-2-22-2−2i−2i2i2i20000−2i2i000000000000000000000000000-2202i−2i00000
χ29222-2-2-22-2-222-2-222-2-2000020000002i−2i002i−2i0000002i2i−2i−2i0000002-20000000000000
χ30222-2-2-22-2-222-2-222-2-2000020000002i−2i002i−2i000000−2i−2i2i2i000000-220000000000000
χ31222-2-2-22-2-222-2-222-2-200002000000−2i2i00−2i2i0000002i2i−2i−2i000000-220000000000000
χ32222-2-2-22-2-222-2-222-2-200002000000−2i2i00−2i2i000000−2i−2i2i2i0000002-20000000000000
χ33222-2-2-22-2-2-222-2-22222i2i−2i−2i-20000−2i2i2i−2i00−2i2i00000000000000000002-20000000000
χ34222-2-2-22-2-2-222-2-22222i2i−2i−2i-20000−2i2i−2i2i002i−2i0000000000000000000-220000000000
χ35222-2-2-22-2-2-222-2-2222−2i−2i2i2i-200002i−2i2i−2i00−2i2i0000000000000000000-220000000000
χ36222-2-2-22-2-2-222-2-2222−2i−2i2i2i-200002i−2i−2i2i002i−2i00000000000000000002-20000000000
χ372-2-2-2-22220-20-2020202-22-2022−2−2000000002-22−2002−22−22-222−2−200000000002−2000
χ382-2-2-2-22220-20-2020202-22-2022−2−200000000-222−2002−22−2-22−2−2220000000000−22000
χ392-2-2-2-22220-20-2020202-22-20−2−222000000002-2−2200−22−222-2−2−2220000000000−22000
χ402-2-2-2-22220-20-2020202-22-20−2−22200000000-22−2200−22−22-2222−2−200000000002−2000
χ412-2-2-2-22220-20-202020-22-22022−2−2000000002-22−200−22−22-22−2−22200000000002−2000
χ422-2-2-2-22220-20-202020-22-22022−2−200000000-222−200−22−222-222−2−20000000000−22000
χ432-2-2-2-22220-20-202020-22-220−2−222000000002-2−22002−22−2-2222−2−20000000000−22000
χ442-2-2-2-22220-20-202020-22-220−2−22200000000-22−22002−22−22-2−2−22200000000002−2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-44-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ4744-44-44-4-44040-40-40000000000000004-4000000000000000000000000000000000
χ4844-44-44-4-44040-40-4000000000000000-44000000000000000000000000000000000
χ4944-44-44-4-4-40-40404000000000000000000000000000000000000000000000002i2−2i20
χ5044-44-44-4-4-40-4040400000000000000000000000000000000000000000000000−2i22i20
χ5144-4-44-4-4440-40-40400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ5244-4-44-4-4440-40-4040000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ5344-4-44-4-44-404040-400000004i−4i4i−4i000000000000000000000000000000000000000
χ5444-4-44-4-44-404040-40000000−4i4i−4i4i000000000000000000000000000000000000000
χ554-444-4-4-44000000000000002i2−2i2−2i22i200000000000022−220000002i−2i−2i2i000000000000000
χ564-444-4-4-44000000000000002i2−2i2−2i22i2000000000000−2222000000−2i2i2i−2i000000000000000
χ574-444-4-4-4400000000000000−2i22i22i2−2i200000000000022−22000000−2i2i2i−2i000000000000000
χ584-444-4-4-4400000000000000−2i22i22i2−2i2000000000000−22220000002i−2i−2i2i000000000000000
χ594-4-444-44-4040-40-40404i−4i−4i4i00000000000000000000000000000000000000000000
χ604-4-444-44-4040-40-4040−4i4i4i−4i00000000000000000000000000000000000000000000
χ614-4-444-44-40-404040-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ624-4-444-44-40-404040-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ634-4-4-4-444404040-40-40000002222−22−220000000000−2222000000000000000000000000000
χ644-4-4-4-444404040-40-4000000−22−222222000000000022−22000000000000000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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