Finite Group Databasebeta

← Group #10855240

Character table — Group #10855240

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order122222223444466666664488881212121244444444444881212121224242424242424244444444488884121212121212121222444882
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1
χ3111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11
χ51111111111111111111111-1-1-1-11111111111-1-1111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-1-1-1111-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1-111-1-111111-1-1-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-1-1111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-111-1-111-1-1-11111-1
χ911111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111-1-11
χ1011111111111111111111-1-1111111111111-1-111-111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1111111-1-1-1-1-1-1
χ1111111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1111-1-111-1
χ1211111111111111111111-1-111111111-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ1311111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111-11111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11-1-11111-1-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-111-1-1-1-111-1-11-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-11111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-222220000-2000022-2-200000000220000-2-2000000000000000-200000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-20000-2000022-2-200000000-2-2000022000000000000000200000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222000020000-2-22200000000-2-20000-2-2000000000000000200000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000020000-2-2220000000022000022000000000000000-200000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-2-2-22-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022-2-2222-2-2-1-1-1-111111111000000000000-2-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-2222-2-2-2-2-1-1-1-111111111000000000000211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-2-2-2-2-2-2-21111-1-1-1-111110000000000002-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-222-222-2-21111-1-1-1-11111000000000000-21111-1-1-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-100002222-2-2-22211111111-1-1-1-1000000000000-2-1-11111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-2-2-2222211111111-1-1-1-1000000000000211-1-1-1-11100000000
χ29222-2-2-22-22-222-22-222-2-2-20000002-2-220000002i−2i000000000000000000022-2-2002i2i−2i−2i00000002i−2i00000000
χ30222-2-2-22-22-222-22-222-2-2-20000002-2-220000002i−2i0000000000000000000-2-22200−2i−2i2i2i00000002i−2i00000000
χ31222-2-2-22-22-222-22-222-2-2-20000002-2-22000000−2i2i000000000000000000022-2-200−2i−2i2i2i0000000−2i2i00000000
χ32222-2-2-22-22-222-22-222-2-2-20000002-2-22000000−2i2i0000000000000000000-2-222002i2i−2i−2i0000000−2i2i00000000
χ332-222-22-2-220000-22-22-22-22-2−i2−i2i2i2000022-2-20000000−i2i22-200−i2−i2i2i2−i2−i2i2i22-2000000−i2i2−i2i200000000000000−i2i20
χ342-222-22-2-220000-22-22-22-22-2−i2−i2i2i20000-2-2220000000−i2i22-200−i2−i2i2i2−i2−i2i2i2-22000000i2−i2i2−i200000000000000i2−i20
χ352-222-22-2-220000-22-22-22-22-2i2i2−i2−i2000022-2-20000000i2−i22-200i2i2−i2−i2i2i2−i2−i22-2000000i2−i2i2−i200000000000000i2−i20
χ362-222-22-2-220000-22-22-22-22-2i2i2−i2−i20000-2-2220000000i2−i22-200i2i2−i2−i2i2i2−i2−i2-22000000−i2i2−i2i200000000000000−i2i20
χ372-222-22-2-220000-22-22-22-2-22−i2−i2i2i2000022-2-20000000i2−i2-2200−i2−i2i2i2i2i2−i2−i2-22000000−i2i2−i2i200000000000000i2−i20
χ382-222-22-2-220000-22-22-22-2-22−i2−i2i2i20000-2-2220000000i2−i2-2200−i2−i2i2i2i2i2−i2−i22-2000000i2−i2i2−i200000000000000−i2i20
χ392-222-22-2-220000-22-22-22-2-22i2i2−i2−i2000022-2-20000000−i2i2-2200i2i2−i2−i2−i2−i2i2i2-22000000i2−i2i2−i200000000000000−i2i20
χ402-222-22-2-220000-22-22-22-2-22i2i2−i2−i20000-2-2220000000−i2i2-2200i2i2−i2−i2−i2−i2i2i22-2000000−i2i2−i2i200000000000000i2−i20
χ412-2-222-22-2222-2-2-222-22-2-2000000-22-222i−2i2i−2i000002i−2i00000000000000002-22-22i−2i0000000002i−2i0000000000
χ422-2-222-22-2222-2-2-222-22-2-2000000-22-222i−2i2i−2i00000−2i2i0000000000000000-22-222i−2i000000000−2i2i0000000000
χ432-2-222-22-2222-2-2-222-22-2-2000000-22-22−2i2i−2i2i000002i−2i0000000000000000-22-22−2i2i0000000002i−2i0000000000
χ442-2-222-22-2222-2-2-222-22-2-2000000-22-22−2i2i−2i2i00000−2i2i00000000000000002-22-2−2i2i000000000−2i2i0000000000
χ452-2-222-22-22-2-222-222-22-2-20000002-22-22i−2i2i−2i2-20000000000000000000000000−2i2i000002-20000000002i−2i000
χ462-2-222-22-22-2-222-222-22-2-20000002-22-22i−2i2i−2i-220000000000000000000000000−2i2i00000-22000000000−2i2i000
χ472-2-222-22-22-2-222-222-22-2-20000002-22-2−2i2i−2i2i2-200000000000000000000000002i−2i000002-2000000000−2i2i000
χ482-2-222-22-22-2-222-222-22-2-20000002-22-2−2i2i−2i2i-2200000000000000000000000002i−2i00000-220000000002i−2i000
χ492-2-2-2-22222-22-22-2-22-2-222002-22-2-2-222000000000000000002-22-20000002-2-220000000000000002-2000000
χ502-2-2-2-22222-22-22-2-22-2-222002-22-2-2-222000000000000000002-22-2000000-222-2000000000000000-22000000
χ512-2-2-2-22222-22-22-2-22-2-22200-22-22-2-22200000000000000000-22-220000002-2-22000000000000000-22000000
χ522-2-2-2-22222-22-22-2-22-2-22200-22-22-2-22200000000000000000-22-22000000-222-20000000000000002-2000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000222200000000-40000-2-2220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000000004000022-2-20000000000000000000000000000000000000
χ55444-4-4-44-444-4-444-444-4-4-4000000-444-4000000000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-24-4-44-22-2-22220000002-2-220000000000000000000000000000000000000000−2i32i3000000000000
χ57444-4-4-44-4-24-4-44-22-2-22220000002-2-2200000000000000000000000000000000000000002i3−2i3000000000000
χ58444-4-4-44-4-2-444-4-22-2-2222000000-222-20000004i−4i000000000000000000000000000000000000−2i2i00000000
χ59444-4-4-44-4-2-444-4-22-2-2222000000-222-2000000−4i4i0000000000000000000000000000000000002i−2i00000000
χ6044-44-4-4-444000044-4-4-4-4400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6144-44-4-4-444000044-4-4-4-440000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6244-4-444-4-4400004-4-4-444-400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ6344-4-444-4-4400004-4-4-444-4002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ6444-4-444-4-4-20000-2222-2-2200−2i22i22i2−2i2000000000000000000023−23i2−i2−i2i2i6−i6i6−i600000000000000000000000000000
χ6544-4-444-4-4-20000-2222-2-2200−2i22i22i2−2i20000000000000000000−2323i2−i2−i2i2−i6i6−i6i600000000000000000000000000000
χ6644-4-444-4-4-20000-2222-2-22002i2−2i2−2i22i2000000000000000000023−23−i2i2i2−i2−i6i6−i6i600000000000000000000000000000
χ6744-4-444-4-4-20000-2222-2-22002i2−2i2−2i22i20000000000000000000−2323−i2i2i2−i2i6−i6i6−i600000000000000000000000000000
χ684-444-44-4-4-200002-22-22-224-4−2i2−2i22i22i2000000000000000−2i22i2-2200i2i2−i2−i2i2i2−i2−i200000000000000000000000000000
χ694-444-44-4-4-200002-22-22-224-42i22i2−2i2−2i20000000000000002i2−2i2-2200−i2−i2i2i2−i2−i2i2i200000000000000000000000000000
χ704-444-44-4-4-200002-22-22-22-44−2i2−2i22i22i20000000000000002i2−2i22-200i2i2−i2−i2−i2−i2i2i200000000000000000000000000000
χ714-444-44-4-4-200002-22-22-22-442i22i2−2i2−2i2000000000000000−2i22i22-200−i2−i2i2i2i2i2−i2−i200000000000000000000000000000
χ724-44-44-4-4440000-4-4-444-44000000000000000000000000000000000000000000022−22−222200000000000000000
χ734-44-44-4-4440000-4-4-444-440000000000000000000000000000000000000000000−222222−2200000000000000000
χ744-4-444-44-4-244-4-42-2-22-2220000002-22-20000000004i−4i0000000000000000000000000000000−2i2i0000000000
χ754-4-444-44-4-244-4-42-2-22-2220000002-22-2000000000−4i4i00000000000000000000000000000002i−2i0000000000
χ764-4-444-44-4-2-4-4442-2-22-222000000-22-2200004-400000000000000000000000000000000-2200000000000000
χ774-4-444-44-4-2-4-4442-2-22-222000000-22-220000-44000000000000000000000000000000002-200000000000000
χ784-4-4-4-444444-44-4-4-44-4-44400000044-4-4000000000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-24-44-422-222-2-2000000-2-22200000000000000000000023−23−232300000000000000000000000000000
χ804-4-4-4-4444-24-44-422-222-2-2000000-2-222000000000000000000000−232323−2300000000000000000000000000000
χ814-4-4-4-4444-2-44-4422-222-2-2004-44-422-2-200000000000000000-22-22000000000000000000000000000000000
χ824-4-4-4-4444-2-44-4422-222-2-200-44-4422-2-2000000000000000002-22-2000000000000000000000000000000000
χ8388-88-8-8-88-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000
χ848-88-88-8-88-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000

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