Finite Group Databasebeta

← Group #10883561

Character table — Group #10883561

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1122222222244444444444668888888888888888888812121216161616161616161616242424242424242424244848
order1222234444644446661212121288222444666688121212121212121288846812121224242424244444888848
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1111-11-11-1-111-1-11-1-11-1-11111-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-1-111-1-1-1-1-1-111-1-111
χ51111111111111111111111-1-111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-111-1-1-111-111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-11-111-1-111111111-1-111-1-1
χ911111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111-1111-1-1-1-1-111-1-1-1-1-1111-1
χ1011111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-11-1-1-111111111-1-1-1-1-1-1-11
χ1111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-11111111-1111-1-1-1-111-1-1-1-111-1-111-11
χ1211111111111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-11111-1-11-1-1111-1-1-1-11-1
χ1311111111111-1-1-1-11111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-11-1-111111-1-1-11
χ1411111111111-1-1-1-11111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-11111111-1
χ1511111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111-1-111-1-11-1
χ1611111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-11-1-1-11111-1-1-111-1-1-11111-11
χ1722222-12222-12222-1-1-1-1-1-1-100222222-1-1-1-122-1-1-1-1-1-1-1-10002-12-1-1-1-1-1-1-1000000000000
χ1822222-12222-12222-1-1-1-1-1-1-10022-2-222-1-1-1-1-2-2-1-1-1-1-1-1-1-1000-21-21111111000000000000
χ1922222-12222-12222-1-1-1-1-1-1-100-2-222-2-2111122-1-1-1-11111000-2-1-2-111-1-111000000000000
χ2022222-12222-12222-1-1-1-1-1-1-100-2-2-2-2-2-21111-2-2-1-1-1-111110002121-1-111-1-1000000000000
χ2122222-12222-1-2-2-2-2-1-1-1-1-1-1-1002222-2-2-1-1-1-1-2-2111111110002-1-2-1-1-11111000000000000
χ2222222-12222-1-2-2-2-2-1-1-1-1-1-1-10022-2-2-2-2-1-1-1-12211111111000-212111-1-1-1-1000000000000
χ2322222-12222-1-2-2-2-2-1-1-1-1-1-1-100-2-222221111-2-21111-1-1-1-1000-2-12-11111-1-1000000000000
χ2422222-12222-1-2-2-2-2-1-1-1-1-1-1-100-2-2-2-2221111221111-1-1-1-100021-21-1-1-1-111000000000000
χ25222-2-222-2-22200002-2-22-22-22200002i−2i00000000002i2i−2i−2i2-2-2000000000000002i−2i000000
χ26222-2-222-2-22200002-2-22-22-2220000−2i2i0000000000−2i−2i2i2i2-2-200000000000000−2i2i000000
χ27222-2-222-2-22200002-2-22-22-2-2-200002i−2i00000000002i2i−2i−2i-22200000000000000−2i2i000000
χ28222-2-222-2-22200002-2-22-22-2-2-20000−2i2i0000000000−2i−2i2i2i-222000000000000002i−2i000000
χ29222-2-22-222-222i2i−2i−2i2-2-2-22-22000000000000002i2i−2i−2i00000000000000000200-200002i−2i00
χ30222-2-22-222-222i2i−2i−2i2-2-2-22-22000000000000002i2i−2i−2i00000000000000000-20020000−2i2i00
χ31222-2-22-222-22−2i−2i2i2i2-2-2-22-2200000000000000−2i−2i2i2i00000000000000000200-20000−2i2i00
χ32222-2-22-222-22−2i−2i2i2i2-2-2-22-2200000000000000−2i−2i2i2i00000000000000000-200200002i−2i00
χ3322-22-2222-2-222i−2i2i−2i-22-222-2-200002-20000002i−2i2i−2i2i−2i0000000020-2002i−2i00000000000000
χ3422-22-2222-2-222i−2i2i−2i-22-222-2-20000-22000000−2i2i2i−2i2i−2i00000000-20200−2i2i00000000000000
χ3522-22-2222-2-22−2i2i−2i2i-22-222-2-200002-2000000−2i2i−2i2i−2i2i0000000020-200−2i2i00000000000000
χ3622-22-2222-2-22−2i2i−2i2i-22-222-2-20000-220000002i−2i−2i2i−2i2i00000000-202002i−2i00000000000000
χ3722-22-22-2-22220000-22-2-2-222222-2000022-2-20000000000-22-2000000000002-2000000000
χ3822-22-22-2-22220000-22-2-2-22222-220000-2-2220000000000-22-200000000000-22000000000
χ3922-22-22-2-22220000-22-2-2-222-2-22-2000022-2-200000000002-2200000000000-22000000000
χ4022-22-22-2-22220000-22-2-2-222-2-2-220000-2-22200000000002-22000000000002-2000000000
χ4122-22-2-122-2-2-12i−2i2i−2i1-11-1-11100002-200−i3i3−i3i32i−2i−ii−ii3−33−30000-101−i3i3−ii3−3000000000000
χ4222-22-2-122-2-2-12i−2i2i−2i1-11-1-11100002-200i3−i3i3−i32i−2i−ii−ii−33−330000-101i3−i3−ii−33000000000000
χ4322-22-2-122-2-2-12i−2i2i−2i1-11-1-1110000-2200−i3i3−i3i3−2i2i−ii−ii3−33−3000010-1i3−i3i−i−33000000000000
χ4422-22-2-122-2-2-12i−2i2i−2i1-11-1-1110000-2200i3−i3i3−i3−2i2i−ii−ii−33−33000010-1−i3i3i−i3−3000000000000
χ4522-22-2-122-2-2-1−2i2i−2i2i1-11-1-11100002-200−i3i3−i3i3−2i2ii−ii−i−33−330000-101−i3i3i−i−33000000000000
χ4622-22-2-122-2-2-1−2i2i−2i2i1-11-1-11100002-200i3−i3i3−i3−2i2ii−ii−i3−33−30000-101i3−i3i−i3−3000000000000
χ4722-22-2-122-2-2-1−2i2i−2i2i1-11-1-1110000-2200−i3i3−i3i32i−2ii−ii−i−33−33000010-1i3−i3−ii3−3000000000000
χ4822-22-2-122-2-2-1−2i2i−2i2i1-11-1-1110000-2200i3−i3i3−i32i−2ii−ii−i3−33−3000010-1−i3i3−ii−33000000000000
χ4922-2-222-22-2222-2-22-2-22-222-2220000000000002-2-220000-2-2200000000000000002-20000
χ5022-2-222-22-2222-2-22-2-22-222-2-2-20000000000002-2-22000022-20000000000000000-220000
χ5122-2-222-22-222-222-2-2-22-222-222000000000000-222-20000-2-220000000000000000-220000
χ5222-2-222-22-222-222-2-2-22-222-2-2-2000000000000-222-2000022-200000000000000002-20000
χ53444444-4-4-4-440000444-4-4-4-400000000000000000000000000000000000000000000000
χ5444444-2-4-4-4-4-20000-2-2-2222200000000−2i32i32i3−2i300000000000000000000000000000000000
χ5544444-2-4-4-4-4-20000-2-2-22222000000002i3−2i3−2i32i300000000000000000000000000000000000
χ56444-4-4-24-4-44-20000-222-22-220000004i−4i0000000000−2i−2i2i2i0000000000000000000000000
χ57444-4-4-24-4-44-20000-222-22-22000000−4i4i00000000002i2i−2i−2i0000000000000000000000000
χ58444-4-4-2-444-4-24i4i−4i−4i-2222-22-200000000000000−2i−2i2i2i00000000000000000000000000000
χ59444-4-4-2-444-4-2−4i−4i4i4i-2222-22-2000000000000002i2i−2i−2i00000000000000000000000000000
χ6044-44-4-2-4-444-200002-2222-2-2004-40000-2-22200000000000000000000000000000000000
χ6144-44-4-2-4-444-200002-2222-2-200-44000022-2-200000000000000000000000000000000000
χ6244-4-4444-44-440000-4-444-4-4400000000000000000000000000000000000000000000000
χ6344-4-44-24-44-4-2000022-2-222-2000000000000000000−2i32i32i3−2i30000000000000000000000000
χ6444-4-44-24-44-4-2000022-2-222-20000000000000000002i3−2i3−2i32i30000000000000000000000000
χ6544-4-44-2-44-44-24-4-4422-22-2-2200000000000000-222-200000000000000000000000000000
χ6644-4-44-2-44-44-2-444-422-22-2-22000000000000002-2-2200000000000000000000000000000
χ678-800080000-800000000000−4i24i2000000000000000000000000000000000000000000000
χ688-800080000-8000000000004i2−4i2000000000000000000000000000000000000000000000
χ6916-16000-8000080000000000000000000000000000000000000000000000000000000000

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