Finite Group Databasebeta

← Group #317685

Character table — Group #317685

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888224444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111
χ91111111111-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11-1111-111-1-111-1-111-1-1
χ101111111111-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1111-11-1-111-1-111-1-111
χ111111111111-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-1-11-1-1-111-1-11111-1-1
χ121111111111-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1111-1-111-1-1-1-111
χ131111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1-1-11-111-1-1-1-111-1-111
χ141111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-11-1-1-11-1-11111-1-111-1-1
χ151111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11-1111-1-1-11111-1-1-1-111
χ161111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1111-1111-1-1-1-11111-1-1
χ1722222222222222-2-2-222-2-2-2-2-222-2-200000000000000000000002200-2-2000000000000
χ1822222222222222-2-2-222-2-2-2-2-222-2-20000000000000000000000-2-20022000000000000
χ192222222222-2-2-2-2-2-2-222-222-2-2-2-22200000000000000000000002-200-22000000000000
χ202222222222-2-2-2-2-2-2-222-222-2-2-2-2220000000000000000000000-22002-2000000000000
χ2122222222-2-22222222-2-2222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ2222222222-2-22222222-2-2222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-22222-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-2-2-2222-2-22-2-2-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-22-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000−2i2i2i−2i
χ29222-22-2-2-20022-2-22-2-20022-20000002i2i−2i−2i00002i2i−2i−2i0000000000000000i2−i2i2−i22−22−20000
χ30222-22-2-2-20022-2-22-2-20022-20000002i2i−2i−2i00002i2i−2i−2i0000000000000000−i2i2−i2i2−22−220000
χ31222-22-2-2-20022-2-22-2-20022-2000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000i2−i2i2−i2−22−220000
χ32222-22-2-2-20022-2-22-2-20022-2000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000−i2i2−i2i22−22−20000
χ33222-22-2-2-200-2-2222-2-2002-220000002i2i−2i−2i0000−2i−2i2i2i0000000000000000i2−i2−i2i22−2−220000
χ34222-22-2-2-200-2-2222-2-2002-220000002i2i−2i−2i0000−2i−2i2i2i0000000000000000−i2i2i2−i2−222−20000
χ35222-22-2-2-200-2-2222-2-2002-22000000−2i−2i2i2i00002i2i−2i−2i0000000000000000i2−i2−i2i2−222−20000
χ36222-22-2-2-200-2-2222-2-2002-22000000−2i−2i2i2i00002i2i−2i−2i0000000000000000−i2i2i2−i22−2−220000
χ3722-22-22-2-22-20000-22-22-22002-200002i−2i2i−2i2i2i−2i−2i00000000002i−2i2-2000000000000000000
χ3822-22-22-2-22-20000-22-22-22002-200002i−2i2i−2i2i2i−2i−2i0000000000−2i2i-22000000000000000000
χ3922-22-22-2-22-20000-22-22-22002-20000−2i2i−2i2i−2i−2i2i2i00000000002i−2i-22000000000000000000
χ4022-22-22-2-22-20000-22-22-22002-20000−2i2i−2i2i−2i−2i2i2i0000000000−2i2i2-2000000000000000000
χ4122-22-22-2-2-220000-22-2-22200-2200002i−2i2i−2i−2i−2i2i2i000000002-20000002i−2i00000000000000
χ4222-22-22-2-2-220000-22-2-22200-2200002i−2i2i−2i−2i−2i2i2i00000000-22000000−2i2i00000000000000
χ4322-22-22-2-2-220000-22-2-22200-220000−2i2i−2i2i2i2i−2i−2i000000002-2000000−2i2i00000000000000
χ4422-22-22-2-2-220000-22-2-22200-220000−2i2i−2i2i2i2i−2i−2i00000000-220000002i−2i00000000000000
χ45444-44-4-4-40044-4-4-44400-4-440000000000000000000000000000000000000000000000
χ46444-44-4-4-400-4-444-44400-44-40000000000000000000000000000000000000000000000
χ4744-44-44-4-44-400004-444-4-400-4400000000000000000000000000000000000000000000
χ4844-44-44-4-4-4400004-44-44-4004-400000000000000000000000000000000000000000000
χ4944-4-4-4-44400000044-400-4000000000000000000004i4i−4i−4i000000000000000000000000
χ5044-4-4-4-44400000044-400-400000000000000000000−4i−4i4i4i000000000000000000000000
χ5144-4-4-4-444000000-4-44004000000004-4-44000000000000000000000000000000000000
χ5244-4-4-4-444000000-4-4400400000000-444-4000000000000000000000000000000000000
χ534-444-4-4-444-40000000-44000000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000
χ544-444-4-4-444-40000000-4400000000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000
χ554-444-4-4-44-4400000004-4000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000
χ564-444-4-4-44-4400000004-400000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000
χ574-44-4-444-40000000000000000004i−4i00002i2−2i22i2−2i222−22−22220000000000000000000000000000
χ584-44-4-444-40000000000000000004i−4i0000−2i22i2−2i22i2−222222−220000000000000000000000000000
χ594-44-4-444-4000000000000000000−4i4i00002i2−2i22i2−2i2−222222−220000000000000000000000000000
χ604-44-4-444-4000000000000000000−4i4i0000−2i22i2−2i22i222−22−22220000000000000000000000000000
χ614-4-444-44-4444-44-4000-4-4000004-4000000000000000000000000000000000000000000
χ624-4-444-44-444-44-44000-4-400000-44000000000000000000000000000000000000000000
χ634-4-444-44-4-4-44-44-40004400000-44000000000000000000000000000000000000000000
χ644-4-444-44-4-4-4-44-4400044000004-4000000000000000000000000000000000000000000
χ654-4-4-444-44004-4-4400000000000000000022−22−2222000022−22−2222000000000000000000000000
χ664-4-4-444-44004-4-44000000000000000000−222222−220000−222222−22000000000000000000000000
χ674-4-4-444-4400-444-400000000000000000022−22−22220000−222222−22000000000000000000000000
χ684-4-4-444-4400-444-4000000000000000000−222222−22000022−22−2222000000000000000000000000

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