Finite Group Databasebeta

← Group #10830664

Character table — Group #10830664

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order1222222234444666666622888812121212444444444446688121224242424242424242222444488884121212121212121222244884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-11111111111-1-111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-1111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11111-1-11-1-111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1-111111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11111-1-1-111-1-111-1
χ911111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-11111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111-1-1-1-11111-111-1-1-1-11
χ1111111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1111-1-1111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11-1-1-1-111111-1-11111-1
χ1311111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1111
χ1411111111111111111111-1-1-1-1-1-111111111-1-111-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1111111-1
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-111-1-111111-1-1-1
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-111-1-1-1-1-1-111111111-1-1111111-1-1-111-1-1111-1-1-1-1-1-11
χ17222222222-2-2-2-22222222220000-2-2-2-222220000-2002200-2-2000000000000-2-2220000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-20000-2002200-2-200000000000022-2-2000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-222220000200-2-20022000000000000-2-2-2-2000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-20000200-2-2002200000000000022220000000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-100002222222-1-122-1-1-1-1-1-1-1-1-1-10000000000002-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-2-2-22-2-2-1-122-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022-2-2222-1-1-2-2-1-111111111000000000000-2-1-11111-1-100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-2222-2-2-1-1-2-2-1-111111111000000000000211-1-1-1-11100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-100002222-2-2-211-2-211-1-1-1-11111000000000000-2-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-2-2-22211-2-211-1-1-1-1111100000000000021111-1-1-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-2-2-2-21122111111-1-1-1-10000000000002-1-111-1-11100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-222-2221122111111-1-1-1-1000000000000-211-1-111-1-100000000
χ29222-2-2-2-22222-2-222-2-2-2-220000002-22-20000002i−2i0000000000000000022-2-200002i2i−2i−2i0002i−2i000000000000
χ30222-2-2-2-22222-2-222-2-2-2-220000002-22-20000002i−2i00000000000000000-2-2220000−2i−2i2i2i0002i−2i000000000000
χ31222-2-2-2-22222-2-222-2-2-2-220000002-22-2000000−2i2i0000000000000000022-2-20000−2i−2i2i2i000−2i2i000000000000
χ32222-2-2-2-22222-2-222-2-2-2-220000002-22-2000000−2i2i00000000000000000-2-22200002i2i−2i−2i000−2i2i000000000000
χ3322-222-2-2-2200002-2-222-2-22-2−i2−i2i2i200002i2i−2i−2i00000002-2−i2i200−i2−i2i2i2−i2−i2i2i20000002i−2i2−22−2000000000000002−20
χ3422-222-2-2-2200002-2-222-2-22-2−i2−i2i2i20000−2i−2i2i2i00000002-2−i2i200−i2−i2i2i2−i2−i2i2i2000000−2i2i−22−2200000000000000−220
χ3522-222-2-2-2200002-2-222-2-22-2i2i2−i2−i200002i2i−2i−2i00000002-2i2−i200i2i2−i2−i2i2i2−i2−i20000002i−2i−22−2200000000000000−220
χ3622-222-2-2-2200002-2-222-2-22-2i2i2−i2−i20000−2i−2i2i2i00000002-2i2−i200i2i2−i2−i2i2i2−i2−i2000000−2i2i2−22−2000000000000002−20
χ3722-222-2-2-2200002-2-222-2-2-22−i2−i2i2i200002i2i−2i−2i0000000-22i2−i200−i2−i2i2i2i2i2−i2−i2000000−2i2i2−22−200000000000000−220
χ3822-222-2-2-2200002-2-222-2-2-22−i2−i2i2i20000−2i−2i2i2i0000000-22i2−i200−i2−i2i2i2i2i2−i2−i20000002i−2i−22−22000000000000002−20
χ3922-222-2-2-2200002-2-222-2-2-22i2i2−i2−i200002i2i−2i−2i0000000-22−i2i200i2i2−i2−i2−i2−i2i2i2000000−2i2i−22−22000000000000002−20
χ4022-222-2-2-2200002-2-222-2-2-22i2i2−i2−i20000−2i−2i2i2i0000000-22−i2i200i2i2−i2−i2−i2−i2i2i20000002i−2i2−22−200000000000000−220
χ412-2-22-2-2222-22-22-2-222-2-22002-22-2-2-222000000000000000002-22-200002-22-2000000000000000000002-2000
χ422-2-22-2-2222-22-22-2-222-2-22002-22-2-2-222000000000000000002-22-20000-22-2200000000000000000000-22000
χ432-2-22-2-2222-22-22-2-222-2-2200-22-22-2-22200000000000000000-22-2200002-22-200000000000000000000-22000
χ442-2-22-2-2222-22-22-2-222-2-2200-22-22-2-22200000000000000000-22-220000-22-22000000000000000000002-2000
χ452-2-2-222-2222-2-22-2-2-2-22220000002-2-222-22-2000002-20000000000000000002-200000000000002-202-200000
χ462-2-2-222-2222-2-22-2-2-2-22220000002-2-222-22-200000-220000000000000000002-20000000000000-220-2200000
χ472-2-2-222-2222-2-22-2-2-2-22220000002-2-22-22-22000002-2000000000000000000-2200000000000002-20-2200000
χ482-2-2-222-2222-2-22-2-2-2-22220000002-2-22-22-2200000-22000000000000000000-220000000000000-2202-200000
χ492-2-2-222-222-222-2-2-2-2-2222000000-222-22-22-22-200000000000000000002-2-22-2200000002-200000000000000
χ502-2-2-222-222-222-2-2-2-2-2222000000-222-22-22-2-220000000000000000000-222-2-220000000-2200000000000000
χ512-2-2-222-222-222-2-2-2-2-2222000000-222-2-22-222-20000000000000000000-222-22-200000002-200000000000000
χ522-2-2-222-222-222-2-2-2-2-2222000000-222-2-22-22-2200000000000000000002-2-222-20000000-2200000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000222200000000-400-2-200220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000000004002200-2-20000000000000000000000000000000000000
χ55444-4-4-4-444-4-44444-4-4-4-44000000-44-44000000000000000000000000000000000000000000000000000000
χ56444-4-4-4-44-244-4-4-2-22222-2000000-22-220000004i−4i00000000000000000000000000000000−2i2i000000000000
χ57444-4-4-4-44-244-4-4-2-22222-2000000-22-22000000−4i4i000000000000000000000000000000002i−2i000000000000
χ58444-4-4-4-44-2-4-444-2-22222-20000002-22-200000000000000000000000000000000000000000023−230000000000
χ59444-4-4-4-44-2-4-444-2-22222-20000002-22-2000000000000000000000000000000000000000000−23230000000000
χ6044-444-4-4-4-20000-222-2-2224-4−2i2−2i22i22i2000000000000000-22−2i22i200i2i2−i2−i2i2i2−i2−i200000000000000000000000000000
χ6144-444-4-4-4-20000-222-2-2224-42i22i2−2i2−2i2000000000000000-222i2−2i200−i2−i2i2i2−i2−i2i2i200000000000000000000000000000
χ6244-444-4-4-4-20000-222-2-222-44−2i2−2i22i22i20000000000000002-22i2−2i200i2i2−i2−i2−i2−i2i2i200000000000000000000000000000
χ6344-444-4-4-4-20000-222-2-222-442i22i2−2i2−2i20000000000000002-2−2i22i200−i2−i2i2i2i2i2−i2−i200000000000000000000000000000
χ6444-4-4-444-4400004-44-4-44-40000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6544-4-4-444-4400004-44-4-44-400000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ664-444-44-4-440000-44-44-44-400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ674-444-44-4-440000-44-44-44-4002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ684-444-44-4-4-200002-22-22-2200−2i22i22i2−2i2000000000000000000023−23i2−i2−i2i2i6−i6i6−i600000000000000000000000000000
χ694-444-44-4-4-200002-22-22-2200−2i22i22i2−2i20000000000000000000−2323i2−i2−i2i2−i6i6−i6i600000000000000000000000000000
χ704-444-44-4-4-200002-22-22-22002i2−2i2−2i22i2000000000000000000023−23−i2i2i2−i2−i6i6−i6i600000000000000000000000000000
χ714-444-44-4-4-200002-22-22-22002i2−2i2−2i22i20000000000000000000−2323−i2i2i2−i2i6−i6i6−i600000000000000000000000000000
χ724-44-44-44-440000-444-44-4-400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ734-44-44-44-440000-444-44-4-40000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ744-4-44-4-44444-44-4-4-444-4-4400000044-4-4000000000000000000000000000000000000000000000000000000
χ754-4-44-4-444-24-44-422-2-222-2000000-2-22200000000000000000000023−23−232300000000000000000000000000000
χ764-4-44-4-444-24-44-422-2-222-2000000-2-222000000000000000000000−232323−2300000000000000000000000000000
χ774-4-44-4-444-2-44-4422-2-222-2004-44-422-2-200000000000000000-22-22000000000000000000000000000000000
χ784-4-44-4-444-2-44-4422-2-222-200-44-4422-2-2000000000000000002-22-2000000000000000000000000000000000
χ794-4-4-444-44-24-4-442222-2-2-2000000-222-20000000004-4000000000000000000000000000000000-2200000000
χ804-4-4-444-44-24-4-442222-2-2-2000000-222-2000000000-440000000000000000000000000000000002-200000000
χ814-4-4-444-44-2-444-42222-2-2-20000002-2-2200004-400000000000000000000000000000000-2200000000000000
χ824-4-4-444-44-2-444-42222-2-2-20000002-2-220000-44000000000000000000000000000000002-200000000000000
χ8388-8-8-888-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-88-88-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000

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