Finite Group Databasebeta

← Group #342211

Character table — Group #342211

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-11-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11111-1-1-1-1-1-111-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1111-1-1-1-1-1-111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-111111111-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-1-11111-1-1111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-111111-1-1-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-1-1-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-111-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11-1-1-1-11-1-1-1-111-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-11-111111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-1111-11111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-111-1-1-1-1-111-1-111-1-111
χ17222222222-222-2-2-22-2-22222-2-2-2-200000000000000002222000000-200-2000000000000
χ18222222222-222-2-2-22-2-22222-2-2-2-20000000000000000-2-2-2-20000002002000000000000
χ19222222222-222-2-2-22-2-2-2-2-2-22222000000000000000022-2-2000000200-2000000000000
χ20222222222-222-2-2-22-2-2-2-2-2-222220000000000000000-2-222000000-2002000000000000
χ2122222222-22-2-2222-2-2-2000000002222-2-2-2-20000000000002222-2-20000000000000000
χ2222222222-22-2-2222-2-2-2000000002222-2-2-2-2000000000000-2-2-2-2220000000000000000
χ2322222222-22-2-2222-2-2-200000000-2-2-2-2222200000000000022-2-2-220000000000000000
χ2422222222-22-2-2222-2-2-200000000-2-2-2-22222000000000000-2-2222-20000000000000000
χ2522-22-2-2-220-20022-2000i2i2−i2−i2i2i2−i2−i222-2-20000i2i2i2i2−i2−i2−i2−i200002-22-2000000000000i2−i2i2−i200
χ2622-22-2-2-220-20022-2000i2i2−i2−i2i2i2−i2−i222-2-20000i2i2i2i2−i2−i2−i2−i20000-22-22000000000000−i2i2−i2i200
χ2722-22-2-2-220-20022-2000i2i2−i2−i2i2i2−i2−i2-2-2220000−i2−i2−i2−i2i2i2i2i200002-2-22000000000000i2−i2−i2i200
χ2822-22-2-2-220-20022-2000i2i2−i2−i2i2i2−i2−i2-2-2220000−i2−i2−i2−i2i2i2i2i20000-222-2000000000000−i2i2i2−i200
χ2922-22-2-2-220-20022-2000−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2−i2−i2i2i2i2i200002-22-2000000000000−i2i2−i2i200
χ3022-22-2-2-220-20022-2000−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2−i2−i2i2i2i2i20000-22-22000000000000i2−i2i2−i200
χ3122-22-2-2-220-20022-2000−i2−i2i2i2−i2−i2i2i2-2-2220000i2i2i2i2−i2−i2−i2−i200002-2-22000000000000−i2i2i2−i200
χ3222-22-2-2-220-20022-2000−i2−i2i2i2−i2−i2i2i2-2-2220000i2i2i2i2−i2−i2−i2−i20000-222-2000000000000i2−i2−i2i200
χ3322-2-22-22-2-202-20002002i−2i2i−2i00002−22−222−2−2i2i2−i2−i2i2i2−i2−i22-22i−2i0000000000002−2i2−i2000000
χ3422-2-22-22-2-202-20002002i−2i2i−2i00002−22−222−2−2i2i2−i2−i2i2i2−i2−i2-22−2i2i000000000000−22−i2i2000000
χ3522-2-22-22-2-202-20002002i−2i2i−2i0000−22−22−2−222−i2−i2i2i2−i2−i2i2i22-22i−2i000000000000−22−i2i2000000
χ3622-2-22-22-2-202-20002002i−2i2i−2i0000−22−22−2−222−i2−i2i2i2−i2−i2i2i2-22−2i2i0000000000002−2i2−i2000000
χ3722-2-22-22-2-202-2000200−2i2i−2i2i00002−22−222−2−2−i2−i2i2i2−i2−i2i2i22-2−2i2i0000000000002−2−i2i2000000
χ3822-2-22-22-2-202-2000200−2i2i−2i2i00002−22−222−2−2−i2−i2i2i2−i2−i2i2i2-222i−2i000000000000−22i2−i2000000
χ3922-2-22-22-2-202-2000200−2i2i−2i2i0000−22−22−2−222i2i2−i2−i2i2i2−i2−i22-2−2i2i000000000000−22i2−i2000000
χ4022-2-22-22-2-202-2000200−2i2i−2i2i0000−22−22−2−222i2i2−i2−i2i2i2−i2−i2-222i−2i0000000000002−2−i2i2000000
χ412-2-2-222-22-2222-22-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000002i−2i02-20000000000
χ422-2-2-222-22-2222-22-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i00000000000−2i2i0-220000000000
χ432-2-2-222-22-2222-22-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000002i−2i0-220000000000
χ442-2-2-222-22-2222-22-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i00000000000−2i2i02-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-4000000000022−22−2222000022−22−2222000022-2-2-2-22200000000000000000000000000
χ47444-4-44-4-4000000000022−22−22220000−222222−220000-2-22222-2-200000000000000000000000000
χ48444-4-44-4-40000000000−222222−22000022−22−22220000-2-22222-2-200000000000000000000000000
χ49444-4-44-4-40000000000−222222−220000−222222−22000022-2-2-2-22200000000000000000000000000
χ5044-44-4-4-440400-4-440002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ5144-44-4-4-440400-4-44000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ5244-4-44-44-440-44000-4000000000022−2222−22−22−2222220000000000000000000000000000000000
χ5344-4-44-44-440-44000-40000000000−2222−22222222−22−220000000000000000000000000000000000
χ544-4444-4-4-4404-4000-400000000000000000022−22−222222−22−222200000000000000000000000000
χ554-4444-4-4-4404-4000-4000000000000000000−222222−22−222222−2200000000000000000000000000
χ564-4444-4-4-4-40-4400040000004i−4i4i−4i000000000000000000000000000000000000000000
χ574-4444-4-4-4-40-440004000000−4i4i−4i4i000000000000000000000000000000000000000000
χ584-44-4-4-44404004-4-40000000000000004i−4i4i−4i0000000000000000000000000000000000
χ594-44-4-4-44404004-4-4000000000000000−4i4i−4i4i0000000000000000000000000000000000
χ604-44-4-4-4440-400-444000000000000000000022−2222−22−2222−222200000000000000000000000000
χ614-44-4-4-4440-400-4440000000000000000000−2222−222222−2222−2200000000000000000000000000
χ624-4-44-444-40000000000000022−22−222200002i2−2i2−2i22i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ634-4-44-444-40000000000000022−22−22220000−2i22i22i2−2i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ644-4-44-444-400000000000000−222222−2200002i2−2i2−2i22i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ654-4-44-444-400000000000000−222222−220000−2i22i22i2−2i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ664-4-4-444-4444-4-4-44-44-4400000000000000000000000000000000000000000000000000
χ674-4-4-444-444-4-4-44-4444-400000000000000000000000000000000000000000000000000
χ684-4-4-444-44-4-4444-44-4-4400000000000000000000000000000000000000000000000000

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