Finite Group Databasebeta

← Group #10855227

Character table — Group #10855227

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order1222222234444666666644888812121212444444444448812121212242424242424242422224444888826612121212121222444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1
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
χ4111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ51111111111111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-11-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-111-1-1-1111
χ81111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-111-1-111-111-1
χ911111111111111111111-1-1111111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111111-1-1-1-1-1-111-1-1-11
χ1011111111111111111111-1-1111111111111-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1111111-1-1-1-1-1-1
χ1111111111111111111111-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111-1-1-1-111-1-1111-1
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1111111
χ1311111111111111111111-1-1-1-1-1-111111111-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1111111-111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-111-1-111-1-1-1-11-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-22222-20000000022-2-2000000000000-2-22200000000000000000-2000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-20000000022-2-200000000000022-2-2000000000000000002000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222200000000-2-222000000000000-2-2-2-2000000000000000002000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000-2-222000000000000222200000000000000000-2000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-100002-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022222-2-2-2-2-1-1-1-111111111000000000000-211-1-1-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-100002-2-2-2-222-2-2-1-1-1-1111111110000000000002-1-11111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-222-2-2-2-2-2-21111-1-1-1-111110000000000002-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-22222-2-21111-1-1-1-11111000000000000-21111-1-1-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-222-2-2222211111111-1-1-1-1000000000000-211-1-111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-222-2-22211111111-1-1-1-10000000000002-1-111-1-11100000000
χ29222-22-2-2-22-22-22222-2-2-2-2000000-2-2220000000002i−2i0000000000000022-2-200002i2i−2i−2i00000002i−2i00000000
χ30222-22-2-2-22-22-22222-2-2-2-2000000-2-2220000000002i−2i00000000000000-2-2220000−2i−2i2i2i00000002i−2i00000000
χ31222-22-2-2-22-22-22222-2-2-2-2000000-2-222000000000−2i2i0000000000000022-2-20000−2i−2i2i2i0000000−2i2i00000000
χ32222-22-2-2-22-22-22222-2-2-2-2000000-2-222000000000−2i2i00000000000000-2-22200002i2i−2i−2i0000000−2i2i00000000
χ3322-22-2-22-2200002-2-22-22-22i−2i22−2−200002i2i−2i−2i0000000−i2i22i−2i0022−2−2−i2−i2i2i20000002-2−i2i2−i2i2000000000000002−20
χ3422-22-2-22-2200002-2-22-22-22i−2i22−2−20000−2i−2i2i2i0000000−i2i22i−2i0022−2−2−i2−i2i2i2000000-22i2−i2i2−i200000000000000−220
χ3522-22-2-22-2200002-2-22-22-22i−2i−2−22200002i2i−2i−2i0000000i2−i22i−2i00−2−222i2i2−i2−i20000002-2i2−i2i2−i200000000000000−220
χ3622-22-2-22-2200002-2-22-22-22i−2i−2−2220000−2i−2i2i2i0000000i2−i22i−2i00−2−222i2i2−i2−i2000000-22−i2i2−i2i2000000000000002−20
χ3722-22-2-22-2200002-2-22-22-2−2i2i22−2−200002i2i−2i−2i0000000i2−i2−2i2i0022−2−2i2i2−i2−i2000000-22−i2i2−i2i200000000000000−220
χ3822-22-2-22-2200002-2-22-22-2−2i2i22−2−20000−2i−2i2i2i0000000i2−i2−2i2i0022−2−2i2i2−i2−i20000002-2i2−i2i2−i2000000000000002−20
χ3922-22-2-22-2200002-2-22-22-2−2i2i−2−22200002i2i−2i−2i0000000−i2i2−2i2i00−2−222−i2−i2i2i2000000-22i2−i2i2−i2000000000000002−20
χ4022-22-2-22-2200002-2-22-22-2−2i2i−2−2220000−2i−2i2i2i0000000−i2i2−2i2i00−2−222−i2−i2i2i20000002-2−i2i2−i2i200000000000000−220
χ412-222-22-2-222-2-22-2-2222-2-20000002-22-22i−2i2i−2i0002i−2i00000000000000002-22-22i−2i000000000002i−2i0000000000
χ422-222-22-2-222-2-22-2-2222-2-20000002-22-22i−2i2i−2i000−2i2i0000000000000000-22-222i−2i00000000000−2i2i0000000000
χ432-222-22-2-222-2-22-2-2222-2-20000002-22-2−2i2i−2i2i0002i−2i0000000000000000-22-22−2i2i000000000002i−2i0000000000
χ442-222-22-2-222-2-22-2-2222-2-20000002-22-2−2i2i−2i2i000−2i2i00000000000000002-22-2−2i2i00000000000−2i2i0000000000
χ452-222-22-2-22-222-2-2-2222-2-2000000-22-222i−2i2i−2i02i−2i0000000000000000000000−2i2i0000000002i−2i0000002-20000
χ462-222-22-2-22-222-2-2-2222-2-2000000-22-222i−2i2i−2i0−2i2i0000000000000000000000−2i2i000000000−2i2i000000-220000
χ472-222-22-2-22-222-2-2-2222-2-2000000-22-22−2i2i−2i2i02i−2i00000000000000000000002i−2i0000000002i−2i000000-220000
χ482-222-22-2-22-222-2-2-2222-2-2000000-22-22−2i2i−2i2i0−2i2i00000000000000000000002i−2i000000000−2i2i0000002-20000
χ492-22-2-2-2222-2-222-2-22-2-222002-22-2-222-2000000000000000002-22-200002-2-22000000000000000002-2000000
χ502-22-2-2-2222-2-222-2-22-2-222002-22-2-222-2000000000000000002-22-20000-222-200000000000000000-22000000
χ512-22-2-2-2222-2-222-2-22-2-22200-22-22-222-200000000000000000-22-2200002-2-2200000000000000000-22000000
χ522-22-2-2-2222-2-222-2-22-2-22200-22-22-222-200000000000000000-22-220000-222-2000000000000000002-2000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022220000-400000000-2-2220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000040000000022-2-20000000000000000000000000000000000000
χ55444-44-4-4-444-44-4444-4-4-4-400000044-4-4000000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-24-44-4-2-2-22222000000-2-22200000000000000000000000000000000000000−2i32i300000000000000
χ57444-44-4-4-4-24-44-4-2-2-22222000000-2-222000000000000000000000000000000000000002i3−2i300000000000000
χ58444-44-4-4-4-2-44-44-2-2-2222200000022-2-20000000004i−4i000000000000000000000000000000000−2i2i00000000
χ59444-44-4-4-4-2-44-44-2-2-2222200000022-2-2000000000−4i4i0000000000000000000000000000000002i−2i00000000
χ6044-44-4-44-4-20000-222-22-224i−4i2222−22−22000000000000000−2i22i2−2i2i00−2−222i2i2−i2−i200000000000000000000000000000
χ6144-44-4-44-4-20000-222-22-224i−4i−22−2222220000000000000002i2−2i2−2i2i0022−2−2−i2−i2i2i200000000000000000000000000000
χ6244-44-4-44-4-20000-222-22-22−4i4i2222−22−220000000000000002i2−2i22i−2i00−2−222−i2−i2i2i200000000000000000000000000000
χ6344-44-4-44-4-20000-222-22-22−4i4i−22−222222000000000000000−2i22i22i−2i0022−2−2i2i2−i2−i200000000000000000000000000000
χ6444-4-4-44-44400004-4-4-44-44000000000000000000000000000000000000000000022−22−222200000000000000000
χ6544-4-4-44-44400004-4-4-44-440000000000000000000000000000000000000000000−222222−2200000000000000000
χ664-444-44-4-4-24-4-4422-2-2-222000000-22-2200000004i−4i000000000000000000000000000000000−2i2i0000000000
χ674-444-44-4-4-24-4-4422-2-2-222000000-22-220000000−4i4i0000000000000000000000000000000002i−2i0000000000
χ684-444-44-4-4-2-444-422-2-2-2220000002-22-2000004i−4i000000000000000000000000000000000−2i2i000000000000
χ694-444-44-4-4-2-444-422-2-2-2220000002-22-200000−4i4i0000000000000000000000000000000002i−2i000000000000
χ704-44-4-4-444444-4-4-4-44-4-4440000004-4-44000000000000000000000000000000000000000000000000000000
χ714-44-4-4-444-244-4-422-222-2-2000000-222-2000000000000000000000−2i32i3−2i32i300000000000000000000000000000
χ724-44-4-4-444-244-4-422-222-2-2000000-222-20000000000000000000002i3−2i32i3−2i300000000000000000000000000000
χ734-44-4-4-444-2-4-44422-222-2-2004-44-42-2-2200000000000000000-22-22000000000000000000000000000000000
χ744-44-4-4-444-2-4-44422-222-2-200-44-442-2-22000000000000000002-22-2000000000000000000000000000000000
χ754-4-444-4-4440000-44-44-4-4400000000004-4-4400000000000000000000000000000000000000000000000000
χ764-4-444-4-4440000-44-44-4-440000000000-444-400000000000000000000000000000000000000000000000000
χ774-4-4-4444-440000-44-4-444-40022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ784-4-4-4444-440000-44-4-444-400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ794-4-4-4444-4-200002-222-2-220022−22−2222000000000000000000023−23−222−26−6−6600000000000000000000000000000
χ804-4-4-4444-4-200002-222-2-220022−22−22220000000000000000000−2323−222−2−666−600000000000000000000000000000
χ814-4-4-4444-4-200002-222-2-2200−222222−22000000000000000000023−232−2−22−666−600000000000000000000000000000
χ824-4-4-4444-4-200002-222-2-2200−222222−220000000000000000000−23232−2−226−6−6600000000000000000000000000000
χ8388-8-8-88-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-400004-44-444-40000000000000000000000000000000000000000000000000000000000000000

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