Finite Group Databasebeta

← Group #10877349

Character table — Group #10877349

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order12222222344446666666224466661212121244444444888812121212121212121212242424242424242444441212121244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1111111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-1-11-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111-1-11-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-111-11111-1-1-1-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-11111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-111-1-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-111
χ17222222222-2-2-2-2222222222-2-22222-2-2-2-2000000000000-2-2000000000000000022-2-20000-20000200000000
χ18222222222-2-2-2-2222222222-2-22222-2-2-2-2000000000000-2-20000000000000000-2-222000020000-200000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-200000000000022000000000000000022-2-2000020000-200000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2220000-20000200000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000-1-1-1-100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-222-2-222-2-211-1-1-1-11111-1-1-1-111110000-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-10000-1-11100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-22222-2-2-2-22211-1-1-1-111111111-1-1-1-1000011-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-11111000011-1-100000000000000
χ29222-2-22-2-2222-2-222-2-22-2-22-22-222-2-222-2-20000000000002-200000000000000000000000002-20002-2000000
χ30222-2-22-2-2222-2-222-2-22-2-22-22-222-2-222-2-20000000000002-20000000000000000000000000-22000-22000000
χ31222-2-22-2-2222-2-222-2-22-2-2-22-22-2-22222-2-2000000000000-2200000000000000000000000002-2000-22000000
χ32222-2-22-2-2222-2-222-2-22-2-2-22-22-2-22222-2-2000000000000-220000000000000000000000000-220002-2000000
χ33222-2-22-2-22-2-22222-2-22-2-22-2-2222-2-2-2-2222i−2i2i−2i00000000-22000000000000000000002i−2i2i−2i00000000000000
χ34222-2-22-2-22-2-22222-2-22-2-22-2-2222-2-2-2-222−2i2i−2i2i00000000-2200000000000000000000−2i2i−2i2i00000000000000
χ35222-2-22-2-22-2-22222-2-22-2-2-222-2-2-222-2-2222i−2i−2i2i000000002-2000000000000000000002i−2i−2i2i00000000000000
χ36222-2-22-2-22-2-22222-2-22-2-2-222-2-2-222-2-222−2i2i2i−2i000000002-200000000000000000000−2i2i2i−2i00000000000000
χ37222-2-22-2-2-1-2-222-1-111-1112-2-22-1-11111-1-12i−2i2i−2i000000001-133−3−333−3−3−i3−i3i3i3−i3−i3i3i30000−ii−ii00000000000000
χ38222-2-22-2-2-1-2-222-1-111-1112-2-22-1-11111-1-12i−2i2i−2i000000001-1−3−333−3−333i3i3−i3−i3i3i3−i3−i30000−ii−ii00000000000000
χ39222-2-22-2-2-1-2-222-1-111-1112-2-22-1-11111-1-1−2i2i−2i2i000000001-133−3−333−3−3i3i3−i3−i3i3i3−i3−i30000i−ii−i00000000000000
χ40222-2-22-2-2-1-2-222-1-111-1112-2-22-1-11111-1-1−2i2i−2i2i000000001-1−3−333−3−333−i3−i3i3i3−i3−i3i3i30000i−ii−i00000000000000
χ41222-2-22-2-2-1-2-222-1-111-111-222-211-1-111-1-12i−2i−2i2i00000000-1133−3−3−3−333−i3−i3i3i3i3i3−i3−i30000−iii−i00000000000000
χ42222-2-22-2-2-1-2-222-1-111-111-222-211-1-111-1-12i−2i−2i2i00000000-11−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000−iii−i00000000000000
χ43222-2-22-2-2-1-2-222-1-111-111-222-211-1-111-1-1−2i2i2i−2i00000000-1133−3−3−3−333i3i3−i3−i3−i3−i3i3i30000i−i−ii00000000000000
χ44222-2-22-2-2-1-2-222-1-111-111-222-211-1-111-1-1−2i2i2i−2i00000000-11−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000i−i−ii00000000000000
χ452-2-22-222-222-22-2-2-22-222-2000000002-22-20000002i−2i00000000002i−2i2i−2i000000002-22-20000000000002i−2i0000
χ462-2-22-222-222-22-2-2-22-222-2000000002-22-20000002i−2i00000000002i−2i2i−2i00000000-22-22000000000000−2i2i0000
χ472-2-22-222-222-22-2-2-22-222-2000000002-22-2000000−2i2i0000000000−2i2i−2i2i000000002-22-2000000000000−2i2i0000
χ482-2-22-222-222-22-2-2-22-222-2000000002-22-2000000−2i2i0000000000−2i2i−2i2i00000000-22-220000000000002i−2i0000
χ492-2-22-222-22-22-22-2-22-222-200000000-22-2200002i−2i000000002i−2i2i−2i0000000000002-2-2200000002i−2i000000000
χ502-2-22-222-22-22-22-2-22-222-200000000-22-2200002i−2i000000002i−2i2i−2i000000000000-222-20000000−2i2i000000000
χ512-2-22-222-22-22-22-2-22-222-200000000-22-220000−2i2i00000000−2i2i−2i2i0000000000002-2-220000000−2i2i000000000
χ522-2-22-222-22-22-22-2-22-222-200000000-22-220000−2i2i00000000−2i2i−2i2i000000000000-222-200000002i−2i000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-222220000000000002200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422222222000000000000-2-200000000000000000000000000000000000000
χ55444-4-44-4-4-244-4-4-2-222-2224-44-4-2-222-2-222000000000000-2200000000000000000000000000000000000000
χ56444-4-44-4-4-244-4-4-2-222-222-44-4422-2-2-2-2220000000000002-200000000000000000000000000000000000000
χ5744-44-4-4-44400004-44-4-4-4400000000000000000000000000000000000000000000000000000000000000−2i22i2
χ5844-44-4-4-44400004-44-4-4-44000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ5944-4-44-44-4400004-4-44-44-400000000000000000000000000000000000000000000000000000000000022−2200
χ6044-4-44-44-4400004-4-44-44-4000000000000000000000000000000000000000000000000000000000000−222200
χ614-4444-4-4-440000-4444-4-4-4000000000000000000000022−220000000000000022−2222−220000000000000000000000
χ624-4444-4-4-440000-4444-4-4-40000000000000000000000−222200000000000000−2222−22220000000000000000000000
χ634-4444-4-4-4-200002-2-2-22220000−2i32i3−2i32i30000000000000022−220000000000i6−i6i6−i6−22−220000000000000000000000
χ644-4444-4-4-4-200002-2-2-22220000−2i32i3−2i32i300000000000000−22220000000000−i6i6−i6i62−22−20000000000000000000000
χ654-4444-4-4-4-200002-2-2-222200002i3−2i32i3−2i30000000000000022−220000000000−i6i6−i6i6−22−220000000000000000000000
χ664-4444-4-4-4-200002-2-2-222200002i3−2i32i3−2i300000000000000−22220000000000i6−i6i6−i62−22−20000000000000000000000
χ674-44-4-4-44440000-44-4-4-4440000000000000000000022−2200000000000022−22−222200000000000000000000000000
χ684-44-4-4-44440000-44-4-4-44400000000000000000000−2222000000000000−222222−2200000000000000000000000000
χ694-44-4-4-444-200002-2222-2-20000−2i32i32i3−2i300000000000022−22000000000000−222−2i6−i6−i6i60000000000000000000000
χ704-44-4-4-444-200002-2222-2-20000−2i32i32i3−2i3000000000000−22220000000000002−2−22−i6i6i6−i60000000000000000000000
χ714-44-4-4-444-200002-2222-2-200002i3−2i3−2i32i300000000000022−22000000000000−222−2−i6i6i6−i60000000000000000000000
χ724-44-4-4-444-200002-2222-2-200002i3−2i3−2i32i3000000000000−22220000000000002−2−22i6−i6−i6i60000000000000000000000
χ734-4-44-444-4-24-44-422-22-2-2200000000-22-220000004i−4i0000000000−2i2i−2i2i000000000000000000000000000000
χ744-4-44-444-4-24-44-422-22-2-2200000000-22-22000000−4i4i00000000002i−2i2i−2i000000000000000000000000000000
χ754-4-44-444-4-2-44-4422-22-2-22000000002-22-200004i−4i00000000−2i2i−2i2i0000000000000000000000000000000000
χ764-4-44-444-4-2-44-4422-22-2-22000000002-22-20000−4i4i000000002i−2i2i−2i0000000000000000000000000000000000
χ774-4-4-444-4444-4-44-4-4-444-44000000004-4-440000000000000000000000000000000000000000000000000000
χ784-4-4-444-444-444-4-4-4-444-4400000000-444-40000000000000000000000000000000000000000000000000000
χ794-4-4-444-44-24-4-44222-2-22-200000000-222-200000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ804-4-4-444-44-24-4-44222-2-22-200000000-222-2000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ814-4-4-444-44-2-444-4222-2-22-2000000002-2-22000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ824-4-4-444-44-2-444-4222-2-22-2000000002-2-220000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ8388-88-8-8-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88-88-8-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000

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