Finite Group Databasebeta

← Group #305658

Character table — Group #305658

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-1111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1111-1-1-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111
χ71111111111111111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-11-1-1111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-11111-1-1-1
χ911111111111111111-1-1-1-11111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11
χ1011111111111111111-1-1-1-11111111-1-111-1-1111111-1-1-1-1111111-1-1-11-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111111-111-1-1-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111111-1-11-1-111-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1111-1-11111-1-111-1
χ172222222222-2-22-22-2-20000-2222222002200-2-200-2-20000000000000-200000000000
χ182222222222-2-22-22-2-20000-22222-2-200-2-2002200-2-20000000000000200000000000
χ192222222222-2-22-22-2-20000-2-2-2-2-22200-2-200-2-200220000000000000200000000000
χ202222222222-2-22-22-2-20000-2-2-2-2-2-2-20022002200220000000000000-200000000000
χ2122222222-2-222-22-22-22222-2000000-2-2002200-2-2000000220000-200000000000000
χ2222222222-2-222-22-22-22222-2000000-2-200-2-20022000000-2-20000200000000000000
χ2322222222-2-222-22-22-2-2-2-2-2-20000002200220022000000-2-20000-200000000000000
χ2422222222-2-222-22-22-2-2-2-2-2-20000002200-2-200-2-2000000220000200000000000000
χ25222-2-2-2-222222-2-2-2-2222-2-2-200002-22-200002-2000000000000000000002-20000000
χ26222-2-2-2-222222-2-2-2-2222-2-2-20000-222-20000-2200000000000000000000-220000000
χ27222-2-2-2-222222-2-2-2-22-2-222-200002-2-2200002-200000000000000000000-220000000
χ28222-2-2-2-222222-2-2-2-22-2-222-20000-22-220000-22000000000000000000002-20000000
χ29222-2-2-2-2222-2-2-22-22-20000200002-2000000-2200002i2i−2i−2i00000000002i−2i000000000
χ30222-2-2-2-2222-2-2-22-22-20000200002-2000000-220000−2i−2i2i2i0000000000−2i2i000000000
χ31222-2-2-2-2222-2-2-22-22-2000020000-220000002-200002i2i−2i−2i0000000000−2i2i000000000
χ32222-2-2-2-2222-2-2-22-22-2000020000-220000002-20000−2i−2i2i2i00000000002i−2i000000000
χ33222-2-2-2-22-2-2222-22-2-222-2-22000000-220000000000000000000002i−2i00000002i−2i000
χ34222-2-2-2-22-2-2222-22-2-222-2-22000000-22000000000000000000000−2i2i0000000−2i2i000
χ35222-2-2-2-22-2-2222-22-2-2-2-22220000002-20000000000000000000002i−2i0000000−2i2i000
χ36222-2-2-2-22-2-2222-22-2-2-2-22220000002-2000000000000000000000−2i2i00000002i−2i000
χ372-2-22-22-22002-2020-202-22-2022−2−20000002i−2i00002−22−22−22i−2ii2i2−i2−i200000000i2−i200000
χ382-2-22-22-22002-2020-202-22-2022−2−2000000−2i2i00002−22−22−2−2i2i−i2−i2i2i200000000−i2i200000
χ392-2-22-22-22002-2020-202-22-20−2−2220000002i−2i0000−22−22−222i−2i−i2−i2i2i200000000−i2i200000
χ402-2-22-22-22002-2020-202-22-20−2−222000000−2i2i0000−22−22−22−2i2ii2i2−i2−i200000000i2−i200000
χ412-2-22-22-22002-2020-20-22-22022−2−20000002i−2i00002−2−22−22−2i2i−i2−i2i2i200000000i2−i200000
χ422-2-22-22-22002-2020-20-22-22022−2−2000000−2i2i00002−2−22−222i−2ii2i2−i2−i200000000−i2i200000
χ432-2-22-22-22002-2020-20-22-220−2−2220000002i−2i0000−222−22−2−2i2ii2i2−i2−i200000000−i2i200000
χ442-2-22-22-22002-2020-20-22-220−2−222000000−2i2i0000−222−22−22i−2i−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-44-4-4-4-4444440000-40000000000000000000000000000000000000000000
χ4744-44-4-44-44-40040-40000000000000004-4000000000000000000000000000000000
χ4844-44-4-44-44-40040-4000000000000000-44000000000000000000000000000000000
χ4944-44-4-44-4-4400-404000000000000000000000000000000000000000000000002i2−2i20
χ5044-44-4-44-4-4400-40400000000000000000000000000000000000000000000000−2i22i20
χ5144-4-444-4-44-400-40400000004i−4i4i−4i000000000000000000000000000000000000000
χ5244-4-444-4-44-400-4040000000−4i4i−4i4i000000000000000000000000000000000000000
χ5344-4-444-4-4-440040-4000000000000000000000000000000022−2222−22000000000000000
χ5444-4-444-4-4-440040-40000000000000000000000000000000−2222−2222000000000000000
χ554-44-4-444-4000000000000002i2−2i2−2i22i2000000000022−22000000002i−2i−2i2i000000000000000
χ564-44-4-444-4000000000000002i2−2i2−2i22i20000000000−222200000000−2i2i2i−2i000000000000000
χ574-44-4-444-400000000000000−2i22i22i2−2i2000000000022−2200000000−2i2i2i−2i000000000000000
χ584-44-4-444-400000000000000−2i22i22i2−2i20000000000−2222000000002i−2i−2i2i000000000000000
χ594-4-44-44-4400-440-4040000002222−22−22000000000000−22220000000000000000000000000
χ604-4-44-44-4400-440-404000000−22−22222200000000000022−220000000000000000000000000
χ614-4-4-44-444004-40-40404-4-4400000000000000000000000000000000000000000000
χ624-4-4-44-444004-40-4040-444-400000000000000000000000000000000000000000000
χ634-4-4-44-44400-44040-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ644-4-4-44-44400-44040-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ658-8888-8-8-8000000000000000000000000000000000000000000000000000000000

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