Finite Group Databasebeta

← Group #10883568

Character table — Group #10883568

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222222222244444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222234444688121266688812121224242424244444668812122424242424244444881212121224242424222444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ4111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ51111111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-111-11111-1-1-1-1
χ61111111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1
χ911111111111-1-111111-1-1-1111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111111-111-1-111-1-1-111-1-1-1-1-1111-1
χ1011111111111-1-111111-1-1-1111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-1-111111-1-1-11
χ1111111111111-1-111111-1-1-1111-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-11-1-111-1-111-1-1-1-111-1-111-11
χ1211111111111-1-111111-1-1-1111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-111-1-11-1
χ1311111111111-1-111111-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1111-1-1-1-1111111-1-1-1-1-1-1-11
χ1411111111111-1-111111-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-11111111-1
χ1511111111111-1-111111-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111111-1-1-11111-1-11-1-1111-1-1-1-11-1
χ1611111111111-1-111111-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11-1-1-11111-1-1-111-1-1-11111-11
χ1722222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1222222-1-122-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ1822222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-122-2-2-2-2-1-122-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ1922222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2222211-2-211-1-111110000-2-2-1-1-1-11111000000000000
χ2022222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-2-211-2-211-1-111110000221111-1-1-1-1000000000000
χ2122222-12222-1-2-2-1-1-1-1-1-2-2-2-1-1-111112222-2-2-1-1-2-2-1-111111100002-2-1-111-1-111000000000000
χ2222222-12222-1-2-2-1-1-1-1-1-2-2-2-1-1-1111122-2-222-1-1-2-2-1-11111110000-2211-1-111-1-1000000000000
χ2322222-12222-1-2-2-1-1-1-1-1-2-2-2-1-1-11111-2-222-2-211221111-1-1-1-10000-22-1-11111-1-1000000000000
χ2422222-12222-1-2-2-1-1-1-1-1-2-2-2-1-1-11111-2-2-2-22211221111-1-1-1-100002-211-1-1-1-111000000000000
χ25222-2-222-2-22222-2-22-2-22-2-22-2222-2-2002i−2i2i−2i0000002-200000000002i−2i2i−2i0000000000000000
χ26222-2-222-2-22222-2-22-2-22-2-22-2222-2-200−2i2i−2i2i0000002-20000000000−2i2i−2i2i0000000000000000
χ27222-2-222-2-222-2-2-2-22-2-2-2222-22-2-222002i−2i−2i2i000000-2200000000002i−2i−2i2i0000000000000000
χ28222-2-222-2-222-2-2-2-22-2-2-2222-22-2-22200−2i2i2i−2i000000-220000000000−2i2i2i−2i0000000000000000
χ29222-2-22-222-2200222-2-2000-22-20000000000002i−2i00002i2i−2i−2i2i2i−2i−2i0000000000200-200000000
χ30222-2-22-222-2200222-2-2000-22-20000000000002i−2i00002i2i−2i−2i−2i−2i2i2i0000000000-200200000000
χ31222-2-22-222-2200222-2-2000-22-2000000000000−2i2i0000−2i−2i2i2i2i2i−2i−2i0000000000-200200000000
χ32222-2-22-222-2200222-2-2000-22-2000000000000−2i2i0000−2i−2i2i2i−2i−2i2i2i0000000000200-200000000
χ33222-2-2-12-2-22-12211-1112-2-2-11-1-1-111002i−2i2i−2i−i3i300−i3i3-11−i3i3−i3i3000000−ii−ii3−33−3000000000000
χ34222-2-2-12-2-22-12211-1112-2-2-11-1-1-111002i−2i2i−2ii3−i300i3−i3-11i3−i3i3−i3000000−ii−ii−33−33000000000000
χ35222-2-2-12-2-22-12211-1112-2-2-11-1-1-11100−2i2i−2i2i−i3i300−i3i3-11−i3i3−i3i3000000i−ii−i−33−33000000000000
χ36222-2-2-12-2-22-12211-1112-2-2-11-1-1-11100−2i2i−2i2ii3−i300i3−i3-11i3−i3i3−i3000000i−ii−i3−33−3000000000000
χ37222-2-2-12-2-22-1-2-211-111-222-11-111-1-1002i−2i−2i2i−i3i300−i3i31-1i3−i3i3−i3000000−iii−i3−3−33000000000000
χ38222-2-2-12-2-22-1-2-211-111-222-11-111-1-1002i−2i−2i2ii3−i300i3−i31-1−i3i3−i3i3000000−iii−i−333−3000000000000
χ39222-2-2-12-2-22-1-2-211-111-222-11-111-1-100−2i2i2i−2i−i3i300−i3i31-1i3−i3i3−i3000000i−i−ii−333−3000000000000
χ40222-2-2-12-2-22-1-2-211-111-222-11-111-1-100−2i2i2i−2ii3−i300i3−i31-1−i3i3−i3i3000000i−i−ii3−3−33000000000000
χ4122-22-22-2-222222-2-2-2-22-22-2-22222-2-2000000000000-2200002-22-200000000000000002-20000
χ4222-22-22-2-222222-2-2-2-22-22-2-22222-2-2000000000000-220000-22-220000000000000000-220000
χ4322-22-22-2-2222-2-2-2-2-2-222-22-222-2-2220000000000002-200002-22-20000000000000000-220000
χ4422-22-22-2-2222-2-2-2-2-2-222-22-222-2-2220000000000002-20000-22-2200000000000000002-20000
χ4522-2-2222-22-2200-2-2-22-200022-200002-200002200-2-20000002i−2i−2i2i0000000000000000002i−2i00
χ4622-2-2222-22-2200-2-2-22-200022-200002-200002200-2-2000000−2i2i2i−2i000000000000000000−2i2i00
χ4722-2-2222-22-2200-2-2-22-200022-20000-220000-2-200220000002i−2i−2i2i000000000000000000−2i2i00
χ4822-2-2222-22-2200-2-2-22-200022-20000-220000-2-20022000000−2i2i2i−2i0000000000000000002i−2i00
χ4922-2-222-22-2222222-22-2-2-22-2-222222000000000000-2-200000000000000000002-202-2000000
χ5022-2-222-22-2222222-22-2-2-22-2-222222000000000000-2-20000000000000000000-220-22000000
χ5122-2-222-22-222-2-222-22-222-2-2-22-2-2-2-20000000000002200000000000000000002-20-22000000
χ5222-2-222-22-222-2-222-22-222-2-2-22-2-2-2-2000000000000220000000000000000000-2202-2000000
χ53444444-4-4-4-4400-4-4444000-4-4-4000000000000000000000000000000000000000000000000
χ5444444-2-4-4-4-4-20022-2-2-200022200000000000000000023−23−232300000000000000000000000000
χ5544444-2-4-4-4-4-20022-2-2-2000222000000000000000000−232323−2300000000000000000000000000
χ56444-4-4-2-444-4-200-2-2-2220002-220000000000004i−4i0000−2i−2i2i2i00000000000000000000000000
χ57444-4-4-2-444-4-200-2-2-2220002-22000000000000−4i4i00002i2i−2i−2i00000000000000000000000000
χ5844-44-4444-4-440044-4-440004-4-4000000000000000000000000000000000000000000000000
χ5944-44-4-244-4-4-200-2-222-2000-2220000000000−2i32i3002i3−2i300000000000000000000000000000000
χ6044-44-4-244-4-4-200-2-222-2000-22200000000002i3−2i300−2i32i300000000000000000000000000000000
χ6144-44-4-2-4-444-2442222-2-44-42-2-2-2-2220000000000002-2000000000000000000000000000000
χ6244-44-4-2-4-444-2-4-42222-24-442-2-222-2-2000000000000-22000000000000000000000000000000
χ6344-4-44-24-44-4-200222-22000-2-2200004-40000-2-2002200000000000000000000000000000000
χ6444-4-44-24-44-4-200222-22000-2-220000-4400002200-2-200000000000000000000000000000000
χ6544-4-44-2-44-44-244-2-22-22-4-4422-2-2-2-2-200000000000022000000000000000000000000000000
χ6644-4-44-2-44-44-2-4-4-2-22-2244-422-22222000000000000-2-2000000000000000000000000000000
χ678-800080000-8−4i24i200000000000−4i24i20000000000000000000000000000000000000000000000
χ688-800080000-84i2−4i2000000000004i2−4i20000000000000000000000000000000000000000000000
χ698-8000-400004−4i24i243−430000000002i2−2i22i6−2i600000000000000000000000000000000000000000000
χ708-8000-400004−4i24i2−43430000000002i2−2i2−2i62i600000000000000000000000000000000000000000000
χ718-8000-4000044i2−4i243−43000000000−2i22i2−2i62i600000000000000000000000000000000000000000000
χ728-8000-4000044i2−4i2−4343000000000−2i22i22i6−2i600000000000000000000000000000000000000000000

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