Finite Group Databasebeta

← Group #10845274

Character table — Group #10845274

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121216161616161616161616242424242424242424242424
order1222222234444666666644441212121222448888121212122424242424242424444444444466121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1111-1-1-1-11-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-11111
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111
χ61111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111-1-111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-1-1-1-1-11111
χ911111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-111-1-111-1-1-111-1-111111-1-1
χ1011111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111111-111-1-111-1-11-1-111-1-1-1-1-111
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-111-11111-1-11-1-111
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1111-1-1-1-1111-1-1-1-111-111-1-1
χ1311111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-11-1-111-1-111-1-1-111-1-1111-1-1
χ1411111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-111111-1-111-1-1-111
χ1511111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111111-1-1-11111-1-1-1-1-1-1-1111-1-111
χ1611111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-1-11111-1-111111-1-1-111-1-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2-20000000022-2-20000000022-2-2000000000000002000000-20000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-20000000022-2-200000000-2-22200000000000000-200000020000
χ19222222222-2-2-2-22222222-2-222-2-2-2-200000000-2-22200000000222200000000000000-2000000-20000
χ20222222222-2-2-2-22222222-2-222-2-2-2-200000000-2-22200000000-2-2-2-200000000000000200000020000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-2-2-2-2-1-1-1-11111111100000000-2-2-1-1-1-11111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-211111111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111100000000221111-1-1-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-222-2-21111-1-1-1-11111000000002-2-1-111-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-2-22211111111-1-1-1-100000000-22-1-11111-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22222-2-21111-1-1-1-1111100000000-2211-1-111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-222-2-22211111111-1-1-1-1000000002-211-1-1-1-111000000000000
χ2922-22-22-2-222-2-2222-2-2-22-200002-22-200002i−2i0000002i2i−2i−2i000000002i2i−2i−2i00000000000002-20000000
χ3022-22-22-2-222-2-2222-2-2-22-200002-22-200002i−2i0000002i2i−2i−2i00000000−2i−2i2i2i0000000000000-220000000
χ3122-22-22-2-222-2-2222-2-2-22-200002-22-20000−2i2i000000−2i−2i2i2i000000002i2i−2i−2i0000000000000-220000000
χ3222-22-22-2-222-2-2222-2-2-22-200002-22-20000−2i2i000000−2i−2i2i2i00000000−2i−2i2i2i00000000000002-20000000
χ332-22-2-222-2222-2-2-2-2-2-22222-22-222-2-2000000002-22-20000000000002i−2i2i−2i000000000002i−2i000000000
χ342-22-2-222-2222-2-2-2-2-2-22222-22-222-2-2000000002-22-2000000000000−2i2i−2i2i00000000000−2i2i000000000
χ352-22-2-222-2222-2-2-2-2-2-2222-22-2222-2-200000000-22-220000000000002i−2i2i−2i00000000000−2i2i000000000
χ362-22-2-222-2222-2-2-2-2-2-2222-22-2222-2-200000000-22-22000000000000−2i2i−2i2i000000000002i−2i000000000
χ372-22-2-222-22-2-222-2-2-2-22222-2-22-2-2222-22-200002-2-220000000000000000002-22-20000000000000000
χ382-22-2-222-22-2-222-2-2-2-22222-2-22-2-222-22-2200002-2-22000000000000000000-22-220000000000000000
χ392-22-2-222-22-2-222-2-2-2-2222-222-2-2-2222-2-220000-222-20000000000000000002-2-220000000000000000
χ402-22-2-222-22-2-222-2-2-2-2222-222-2-2-222-222-20000-222-2000000000000000000-222-20000000000000000
χ412-22-2-222-2-1-2-2221111-1-1-12-2-2211-1-12-22-20000-111-1−i3i3−i3i3−i3−i3i3i30000000000-11-11−i3i3−i3i3000000000000
χ422-22-2-222-2-1-2-2221111-1-1-12-2-2211-1-12-22-20000-111-1i3−i3i3−i3i3i3−i3−i30000000000-11-11i3−i3i3−i3000000000000
χ432-22-2-222-2-1-2-2221111-1-1-12-2-2211-1-1-22-220000-111-1−i3i3−i3i3−i3−i3i3i300000000001-11-1i3−i3i3−i3000000000000
χ442-22-2-222-2-1-2-2221111-1-1-12-2-2211-1-1-22-220000-111-1i3−i3i3−i3i3i3−i3−i300000000001-11-1−i3i3−i3i3000000000000
χ452-22-2-222-2-1-2-2221111-1-1-1-222-211-1-12-2-2200001-1-11−i3i3−i3i3i3i3−i3−i30000000000-111-1−i3i3i3−i3000000000000
χ462-22-2-222-2-1-2-2221111-1-1-1-222-211-1-12-2-2200001-1-11i3−i3i3−i3−i3−i3i3i30000000000-111-1i3−i3−i3i3000000000000
χ472-22-2-222-2-1-2-2221111-1-1-1-222-211-1-1-222-200001-1-11−i3i3−i3i3i3i3−i3−i300000000001-1-11i3−i3−i3i3000000000000
χ482-22-2-222-2-1-2-2221111-1-1-1-222-211-1-1-222-200001-1-11i3−i3i3−i3−i3−i3i3i300000000001-1-11−i3i3i3−i3000000000000
χ492-2-2-222-2222-22-2-2-222-22-200002-2-220000002i−2i000000002i−2i2i−2i00002-2-220000000000000002i−2i00000
χ502-2-2-222-2222-22-2-2-222-22-200002-2-220000002i−2i000000002i−2i2i−2i0000-222-2000000000000000−2i2i00000
χ512-2-2-222-2222-22-2-2-222-22-200002-2-22000000−2i2i00000000−2i2i−2i2i00002-2-22000000000000000−2i2i00000
χ522-2-2-222-2222-22-2-2-222-22-200002-2-22000000−2i2i00000000−2i2i−2i2i0000-222-20000000000000002i−2i00000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4222200000000-2-22200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422220000000022-2-200000000000000000000000000000000000000
χ55444-4-4-4-44400004-44-44-4-40000000000000000000000000000004-400000000000000000000000000
χ56444-4-4-4-44400004-44-44-4-4000000000000000000000000000000-4400000000000000000000000000
χ5744-44-44-4-44-444-444-4-4-44-40000-44-4400000000000000000000000000000000000000000000000000
χ5844-44-44-4-4-24-4-44-2-2222-220000-22-2200004i−4i000000−2i−2i2i2i0000000000000000000000000000000000
χ5944-44-44-4-4-24-4-44-2-2222-220000-22-220000−4i4i0000002i2i−2i−2i0000000000000000000000000000000000
χ6044-44-44-4-4-2-444-4-2-2222-2200002-22-2000000000000000023−23−2323000000000000000000000000000000
χ6144-44-44-4-4-2-444-4-2-2222-2200002-22-20000000000000000−232323−23000000000000000000000000000000
χ6244-4-44-44-4400004-4-44-4-4400000000000000000000000000000000000000000000000000000000−2i22i2
χ6344-4-44-44-4400004-4-44-4-44000000000000000000000000000000000000000000000000000000002i2−2i2
χ644-4444-4-4-440000-44-444-4-400000000000000000000000000004-40000000000000000000000000000
χ654-4444-4-4-440000-44-444-4-40000000000000000000000000000-440000000000000000000000000000
χ664-44-4-444-4-244-4-42222-2-2-24-44-4-2-22200000000-22-2200000000000000000000000000000000000000
χ674-44-4-444-4-244-4-42222-2-2-2-44-44-2-222000000002-22-200000000000000000000000000000000000000
χ684-4-44-4-44440000-444-4-4-4400000000000000000000000000000000000000000000000000000022−2200
χ694-4-44-4-44440000-444-4-4-44000000000000000000000000000000000000000000000000000000−222200
χ704-4-4-444-444-44-44-4-444-44-40000-444-400000000000000000000000000000000000000000000000000
χ714-4-4-444-44-24-44-422-2-22-220000-222-20000004i−4i00000000−2i2i−2i2i000000000000000000000000000000
χ724-4-4-444-44-24-44-422-2-22-220000-222-2000000−4i4i000000002i−2i2i−2i000000000000000000000000000000
χ734-4-4-444-44-2-44-4422-2-22-2200002-2-2200000000000023−23−23230000000000000000000000000000000000
χ744-4-4-444-44-2-44-4422-2-22-2200002-2-22000000000000−232323−230000000000000000000000000000000000
χ75888-8-8-8-88-40000-44-44-4440000000000000000000000000000000000000000000000000000000000
χ7688-8-88-88-8-40000-444-444-40000000000000000000000000000000000000000000000000000000000
χ778-8888-8-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000
χ788-8-88-8-888-400004-4-4444-40000000000000000000000000000000000000000000000000000000000

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