Finite Group Databasebeta

← Group #10883562

Character table — Group #10883562

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222222222244444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222234444666886688812121212242424242224446688121224242424242444446688121224242424244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111-1-11-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-111-1-1
χ91111111111111-1-111-1-1-11111-1-1-1-1111-1-1111-1-111-1-1-1-1-1-11111111-1-1-111-1-1-1-111-1-1-1-1111-1
χ101111111111111-1-111-1-1-11111-1-1-1-1111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-11111-1-1-11
χ111111111111111-1-111-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111111111-11-1-1-1-1111111-1-1-1-1-1-1-11
χ121111111111111-1-111-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-11-1-1-1-111-1-1-1-11111111-1
χ131111111111111-1-111-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1111-1-111-1-1-1-111-1-111-11
χ141111111111111-1-111-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-111-1-11-1
χ151111111111111-1-111-1-1-11111-1-1-1-1-1-1-111-1-1-111-1-1-1-111111111-1-11-11111-1-111-1-111-1-1-1-11-1
χ161111111111111-1-111-1-1-11111-1-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-11-11111-1-1-1-111-1-11111-11
χ1722222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1222222-1-122-1-1-1-1-1-1-1-10000-1-122-1-1-1-1-1-1000000000000
χ1822222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-122-222-211-2-211-1-111110000-1-1-2-2-1-11111000000000000
χ1922222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-22-2-22-1-122-1-1-1-1-1-1-1-1000011-2-2111111000000000000
χ2022222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-211-2-211-1-111110000112211-1-1-1-1000000000000
χ2122222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-11111222-2-22-1-1-2-2-1-11111110000-1-12-211-1-111000000000000
χ2222222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-1111122-2-2-2-211221111-1-1-1-10000-1-1-221111-1-1000000000000
χ2322222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-11111-2-22222-1-1-2-2-1-1111111000011-22-1-111-1-1000000000000
χ2422222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-11111-2-2-222-211221111-1-1-1-10000112-2-1-1-1-111000000000000
χ25222-2-222-2-2222222-2-22-2-22-22-22222000000000000-2-2000000000000000000002i−2i2i−2i000000
χ26222-2-222-2-2222222-2-22-2-22-22-22222000000000000-2-200000000000000000000−2i2i−2i2i000000
χ27222-2-222-2-22222-2-2-2-2-2222-22-2-2-2-2-200000000000022000000000000000000002i−2i−2i2i000000
χ28222-2-222-2-22222-2-2-2-2-2222-22-2-2-2-2-20000000000002200000000000000000000−2i2i2i−2i000000
χ29222-2-22-222-222200-2-2000-22-22000000200-22200-2-20000002i2i−2i−2i0000000000000000002i−2i00
χ30222-2-22-222-222200-2-2000-22-22000000200-22200-2-2000000−2i−2i2i2i000000000000000000−2i2i00
χ31222-2-22-222-222200-2-2000-22-22000000-2002-2-200220000002i2i−2i−2i000000000000000000−2i2i00
χ32222-2-22-222-222200-2-2000-22-22000000-2002-2-20022000000−2i−2i2i2i0000000000000000002i−2i00
χ3322-22-222-22-2-2-22002-200022-2-20000000000002i−2i00002i2i−2i−2i2i−2i2i−2i00000000002-20000000000
χ3422-22-222-22-2-2-22002-200022-2-20000000000002i−2i00002i2i−2i−2i−2i2i−2i2i0000000000-220000000000
χ3522-22-222-22-2-2-22002-200022-2-2000000000000−2i2i0000−2i−2i2i2i2i−2i2i−2i0000000000-220000000000
χ3622-22-222-22-2-2-22002-200022-2-2000000000000−2i2i0000−2i−2i2i2i−2i2i−2i2i00000000002-20000000000
χ3722-22-22-22-22-2-22222-2-22-2-2-22222-2-22-202-200000002-2000000002-2002-20000000000000000
χ3822-22-22-22-22-2-22222-2-22-2-2-22222-2-2-220-2200000002-200000000-2200-220000000000000000
χ3922-22-22-22-22-2-22-2-22-22-22-2-222-2-2222-20-220000000-22000000002-200-220000000000000000
χ4022-22-22-22-22-2-22-2-22-22-22-2-222-2-222-2202-20000000-2200000000-22002-20000000000000000
χ4122-22-2-1-22-2211-122-11-22-211-1-1-1-1112-202-20−i3i300−i3i3-11−i3i3−i3i30000-1100-11−i3i3−i3i3000000000000
χ4222-22-2-1-22-2211-122-11-22-211-1-1-1-1112-202-20i3−i300i3−i3-11i3−i3i3−i30000-1100-11i3−i3i3−i3000000000000
χ4322-22-2-1-22-2211-122-11-22-211-1-1-1-111-220-220−i3i300−i3i3-11−i3i3−i3i300001-1001-1i3−i3i3−i3000000000000
χ4422-22-2-1-22-2211-122-11-22-211-1-1-1-111-220-220i3−i300i3−i3-11i3−i3i3−i300001-1001-1−i3i3−i3i3000000000000
χ4522-22-2-1-22-2211-1-2-2-112-2211-1-111-1-12-20-220−i3i300−i3i31-1i3−i3i3−i30000-11001-1−i3i3i3−i3000000000000
χ4622-22-2-1-22-2211-1-2-2-112-2211-1-111-1-12-20-220i3−i300i3−i31-1−i3i3−i3i30000-11001-1i3−i3−i3i3000000000000
χ4722-22-2-1-22-2211-1-2-2-112-2211-1-111-1-1-2202-20−i3i300−i3i31-1i3−i3i3−i300001-100-11i3−i3−i3i3000000000000
χ4822-22-2-1-22-2211-1-2-2-112-2211-1-111-1-1-2202-20i3−i300i3−i31-1−i3i3−i3i300001-100-11−i3i3i3−i3000000000000
χ4922-2-222-2-222-2-2222-22-2-22-222-222-2-2000000000000-2200002-2-2200000000000000002-20000
χ5022-2-222-2-222-2-2222-22-2-22-222-222-2-2000000000000-220000-222-20000000000000000-220000
χ5122-2-222-2-222-2-22-2-2-2222-2-222-2-2-2220000000000002-200002-2-220000000000000000-220000
χ5222-2-222-2-222-2-22-2-2-2222-2-222-2-2-2220000000000002-20000-222-200000000000000002-20000
χ53444444-4-4-4-44440044000-4-4-4-4000000000000000000000000000000000000000000000000
χ5444444-2-4-4-4-4-2-2-200-2-2000222200000000000000000023−23−232300000000000000000000000000
χ5544444-2-4-4-4-4-2-2-200-2-20002222000000000000000000−232323−2300000000000000000000000000
χ56444-4-4-24-4-44-2-2-244224-4-4-22-22-2-2-2-200000000000022000000000000000000000000000000
χ57444-4-4-24-4-44-2-2-2-4-422-444-22-222222000000000000-2-2000000000000000000000000000000
χ58444-4-4-2-444-4-2-2-200220002-22-2000000400-4-2-2002200000000000000000000000000000000
χ59444-4-4-2-444-4-2-2-200220002-22-2000000-40042200-2-200000000000000000000000000000000
χ6044-44-4-24-44-422-200-22000-2-2220000000000004i−4i0000−2i−2i2i2i00000000000000000000000000
χ6144-44-4-24-44-422-200-22000-2-222000000000000−4i4i00002i2i−2i−2i00000000000000000000000000
χ6244-4-44444-4-4-4-4400-440004-4-44000000000000000000000000000000000000000000000000
χ6344-4-44-244-4-422-2002-2000-222-20000000000−2i32i3002i3−2i300000000000000000000000000000000
χ6444-4-44-244-4-422-2002-2000-222-200000000002i3−2i300−2i32i300000000000000000000000000000000
χ6544-4-44-2-4-44422-2442-2-4-442-2-22-2-2220000000000002-2000000000000000000000000000000
χ6644-4-44-2-4-44422-2-4-42-244-42-2-2222-2-2000000000000-22000000000000000000000000000000
χ678-80008000000-8−4i24i2000000000−4i24i20000000000000000000000000000000000000000000000
χ688-80008000000-84i2−4i20000000004i2−4i20000000000000000000000000000000000000000000000
χ698-8000-40000−4i34i34−4i24i20000000002i2−2i226−2600000000000000000000000000000000000000000000
χ708-8000-40000−4i34i344i2−4i2000000000−2i22i2−262600000000000000000000000000000000000000000000
χ718-8000-400004i3−4i34−4i24i20000000002i2−2i2−262600000000000000000000000000000000000000000000
χ728-8000-400004i3−4i344i2−4i2000000000−2i22i226−2600000000000000000000000000000000000000000000

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