Finite Group Databasebeta

← Group #308183

Character table — Group #308183

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-1-1-111-1111-1-111-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1111111-1-1-1
χ911111111111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1011111111111111111-1-1-1-11111111-1-11111-1-11111-1-1-1-1111111-1-1-1-11-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-111-1-111-1-1-1-11111-1-1111111-1-1-1111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-11111-1-111-1
χ17222222222-2-22-222-2-20000-222222200-2-2-2-200-2-2000000000000000020000000000
χ18222222222-2-22-222-2-20000-22222-2-200222200-2-20000000000000000-20000000000
χ19222222222-2-22-222-2-20000-2-2-2-2-22200-2-22200220000000000000000-20000000000
χ20222222222-2-22-222-2-20000-2-2-2-2-2-2-20022-2-20022000000000000000020000000000
χ2122222222-222-22-2-22-22222-2000000-2-200002200-2-2000022000000000-2000000000
χ2222222222-222-22-2-22-22222-2000000-2-20000-2-200220000-2-20000000002000000000
χ2322222222-222-22-2-22-2-2-2-2-2-20000002200002200220000-2-2000000000-2000000000
χ2422222222-222-22-2-22-2-2-2-2-2-2000000220000-2-200-2-20000220000000002000000000
χ25222-22-2-2-2222-2-22-2-220000-200002-2002-20000000022-2-20000002-20000000000000
χ26222-22-2-2-2222-2-22-2-220000-200002-2002-200000000-2-222000000-220000000000000
χ27222-22-2-2-2222-2-22-2-220000-20000-2200-220000000022-2-2000000-220000000000000
χ28222-22-2-2-2222-2-22-2-220000-20000-2200-2200000000-2-2220000002-20000000000000
χ29222-22-2-2-22-2-2-222-22-22i2i−2i−2i200002-22i−2i-22000000000000000000002i−2i00000000000
χ30222-22-2-2-22-2-2-222-22-22i2i−2i−2i20000-222i−2i2-200000000000000000000−2i2i00000000000
χ31222-22-2-2-22-2-2-222-22-2−2i−2i2i2i200002-2−2i2i-2200000000000000000000−2i2i00000000000
χ32222-22-2-2-22-2-2-222-22-2−2i−2i2i2i20000-22−2i2i2-2000000000000000000002i−2i00000000000
χ33222-22-2-2-2-2-2-222-22222i2i−2i−2i-2000000−2i2i000000000000000000000000002i−2i002-2000
χ34222-22-2-2-2-2-2-222-22222i2i−2i−2i-2000000−2i2i00000000000000000000000000−2i2i00-22000
χ35222-22-2-2-2-2-2-222-2222−2i−2i2i2i-20000002i−2i000000000000000000000000002i−2i00-22000
χ36222-22-2-2-2-2-2-222-2222−2i−2i2i2i-20000002i−2i00000000000000000000000000−2i2i002-2000
χ372-2-2-2222-202-20200-202-22-2022−2−2000000002i−2i2−2002−22−22i−2ii2i2−i2−i200000000i2−i200000
χ382-2-2-2222-202-20200-202-22-2022−2−200000000−2i2i2−2002−22−2−2i2i−i2−i2i2i200000000−i2i200000
χ392-2-2-2222-202-20200-202-22-20−2−222000000002i−2i−2200−22−222i−2i−i2−i2i2i200000000−i2i200000
χ402-2-2-2222-202-20200-202-22-20−2−22200000000−2i2i−2200−22−22−2i2ii2i2−i2−i200000000i2−i200000
χ412-2-2-2222-202-20200-20-22-22022−2−2000000002i−2i2−200−22−22−2i2i−i2−i2i2i200000000i2−i200000
χ422-2-2-2222-202-20200-20-22-22022−2−200000000−2i2i2−200−22−222i−2ii2i2−i2−i200000000−i2i200000
χ432-2-2-2222-202-20200-20-22-220−2−222000000002i−2i−22002−22−2−2i2ii2i2−i2−i200000000−i2i200000
χ442-2-2-2222-202-20200-20-22-220−2−22200000000−2i2i−22002−22−22i−2i−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-4-4444-4-44-4-4000040000000000000000000000000000000000000000000
χ4744-44-44-4-440040-4-4000000000000000004-40000000000000000000000000000000
χ4844-44-44-4-440040-4-400000000000000000-440000000000000000000000000000000
χ4944-44-44-4-4-400-4044000000000000000000000000000000000000000000000002i2−2i20
χ5044-44-44-4-4-400-404400000000000000000000000000000000000000000000000−2i22i20
χ5144-4-4-4-444400-40-4400000004-44-4000000000000000000000000000000000000000
χ5244-4-4-4-444400-40-440000000-44-44000000000000000000000000000000000000000
χ5344-4-4-4-444-400404-4000000000000000000000000000000022−2222−22000000000000000
χ5444-4-4-4-444-400404-40000000000000000000000000000000−2222−2222000000000000000
χ554-444-4-44-40000000000000022−22−22220000000000002i2−2i20000002i−2i−2i2i000000000000000
χ564-444-4-44-40000000000000022−22−2222000000000000−2i22i2000000−2i2i2i−2i000000000000000
χ574-444-4-44-400000000000000−222222−220000000000002i2−2i2000000−2i2i2i−2i000000000000000
χ584-444-4-44-400000000000000−222222−22000000000000−2i22i20000002i−2i−2i2i000000000000000
χ594-4-444-4-4404-40-400400000000000000000000000022−22−2222000000000000000000000
χ604-4-444-4-4404-40-4004000000000000000000000000−222222−22000000000000000000000
χ614-4-444-4-440-440400-404i−4i−4i4i00000000000000000000000000000000000000000000
χ624-4-444-4-440-440400-40−4i4i4i−4i00000000000000000000000000000000000000000000
χ634-4-4-4444-40-440-40040000002222−22−220000000000−2222000000000000000000000000000
χ644-4-4-4444-40-440-4004000000−22−222222000000000022−22000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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