Finite Group Databasebeta

← Group #10844916

Character table — Group #10844916

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121212121212161616161616161616162424242424244848
order12222222344446666666888812121212224444881212121224242424242424244444444488882466661212121244448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-1111111-1-1
χ51111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111111-1-111-1-1111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-1-1-11111
χ911111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-111-1-111-1-1-11
χ1011111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1111-1
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-11111-1-1-1-111-1-111-11
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111111-11111-1-1-1-1-1-111-1-11-1
χ1311111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-11111-1-111-1-1-1-11-1
χ1411111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-11111-11
χ1511111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-11-1-1-1-11111-1-111111-1
χ1611111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-11-1-1-1-1111111-1-1-1-1-11
χ17222222222-2-2-2-222222220000-2-2-2-200002-20022-2-20000000022-2-2-2-2220000000000000000000000
χ18222222222-2-2-2-222222220000-2-2-2-200002-20022-2-200000000-2-22222-2-20000000000000000000000
χ19222222222-2-2-2-222222220000-2-2-2-20000-2200-2-222000000002222-2-2-2-20000000000000000000000
χ20222222222-2-2-2-222222220000-2-2-2-20000-2200-2-22200000000-2-2-2-222220000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-2-2-2-21111-1-1-1-11111000000000000-2-2-1-111-1-11100000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-111110000000000002211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-222-2-2-1-1-1-111111111000000000000-22-1-11111-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-2-22211111111-1-1-1-10000000000002-2-1-1-1-1111100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22222-2-2-1-1-1-1111111110000000000002-211-1-1-1-11100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-222-2-22211111111-1-1-1-1000000000000-221111-1-1-1-100000000
χ2922-222-2-2-222-2-22222-2-2-2-22i2i−2i−2i2-22-22-22i−2i000000002i2i−2i−2i0000000000000000002-2002i−2i0000000000
χ3022-222-2-2-222-2-22222-2-2-2-22i2i−2i−2i2-22-2-22−2i2i000000002i2i−2i−2i000000000000000000-2200−2i2i0000000000
χ3122-222-2-2-222-2-22222-2-2-2-2−2i−2i2i2i2-22-22-2−2i2i00000000−2i−2i2i2i0000000000000000002-200−2i2i0000000000
χ3222-222-2-2-222-2-22222-2-2-2-2−2i−2i2i2i2-22-2-222i−2i00000000−2i−2i2i2i000000000000000000-22002i−2i0000000000
χ3322-222-2-2-2-12-2-22-1-1-111112i2i−2i−2i-11-112-22i−2i00003−33−3−i−iii−i3−i3i3i300000000000000-11−i3i3−ii3−300000000
χ3422-222-2-2-2-12-2-22-1-1-111112i2i−2i−2i-11-112-22i−2i0000−33−33−i−iiii3i3−i3−i300000000000000-11i3−i3−ii−3300000000
χ3522-222-2-2-2-12-2-22-1-1-111112i2i−2i−2i-11-11-22−2i2i00003−33−3−i−iii−i3−i3i3i3000000000000001-1i3−i3i−i−3300000000
χ3622-222-2-2-2-12-2-22-1-1-111112i2i−2i−2i-11-11-22−2i2i0000−33−33−i−iiii3i3−i3−i3000000000000001-1−i3i3i−i3−300000000
χ3722-222-2-2-2-12-2-22-1-1-11111−2i−2i2i2i-11-112-2−2i2i00003−33−3ii−i−ii3i3−i3−i300000000000000-11i3−i3i−i3−300000000
χ3822-222-2-2-2-12-2-22-1-1-11111−2i−2i2i2i-11-112-2−2i2i0000−33−33ii−i−i−i3−i3i3i300000000000000-11−i3i3i−i−3300000000
χ3922-222-2-2-2-12-2-22-1-1-11111−2i−2i2i2i-11-11-222i−2i00003−33−3ii−i−ii3i3−i3−i3000000000000001-1−i3i3−ii−3300000000
χ4022-222-2-2-2-12-2-22-1-1-11111−2i−2i2i2i-11-11-222i−2i0000−33−33ii−i−i−i3−i3i3i3000000000000001-1i3−i3−ii3−300000000
χ412-22-22-22-222-22-2-2-22-2-2222-22-22-2-220000000000002-22-2000000000000000000000000002i−2i2i−2i0000
χ422-22-22-22-222-22-2-2-22-2-2222-22-22-2-220000000000002-22-200000000000000000000000000−2i2i−2i2i0000
χ432-22-22-22-222-22-2-2-22-2-222-22-222-2-22000000000000-22-22000000000000000000000000002i−2i−2i2i0000
χ442-22-22-22-222-22-2-2-22-2-222-22-222-2-22000000000000-22-2200000000000000000000000000−2i2i2i−2i0000
χ452-2-2-222-22222-2-2-2-2222-2-22i−2i−2i2i22-2-20000000000002i−2i−2i2i0000002-2002-20000000000000000002i−2i00
χ462-2-2-222-22222-2-2-2-2222-2-22i−2i−2i2i22-2-20000000000002i−2i−2i2i000000-2200-22000000000000000000−2i2i00
χ472-2-2-222-22222-2-2-2-2222-2-2−2i2i2i−2i22-2-2000000000000−2i2i2i−2i0000002-2002-2000000000000000000−2i2i00
χ482-2-2-222-22222-2-2-2-2222-2-2−2i2i2i−2i22-2-2000000000000−2i2i2i−2i000000-2200-220000000000000000002i−2i00
χ492-2-2-222-222-2-222-2-2222-2-20000-2-2220000002-2000000002-22-2002-200-2222-2-2000000000000000000
χ502-2-2-222-222-2-222-2-2222-2-20000-2-2220000002-2000000002-22-200-22002-2-2-222000000000000000000
χ512-2-2-222-222-2-222-2-2222-2-20000-2-222000000-2200000000-22-22002-200-22-2-222000000000000000000
χ522-2-2-222-222-2-222-2-2222-2-20000-2-222000000-2200000000-22-2200-22002-222-2-2000000000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-20000222200004-400-2-22200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000-440022-2-200000000000000000000000000000000000000
χ55444-4-4-4-44400004-4-44-44-400000000000000000000000000004i−4i0000000000000000000000000000
χ56444-4-4-4-44400004-4-44-44-40000000000000000000000000000−4i4i0000000000000000000000000000
χ5744-444-4-4-44-444-4444-4-4-4-40000-44-4400000000000000000000000000000000000000000000000000
χ5844-444-4-4-4-2-444-4-2-2-2222200002-22-20000000023−23−232300000000000000000000000000000000000000
χ5944-444-4-4-4-2-444-4-2-2-2222200002-22-200000000−232323−2300000000000000000000000000000000000000
χ6044-4-4-444-4400004-4-4-44-44000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ6144-4-4-444-4400004-4-4-44-440000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ624-444-44-4-440000-44-4-444-4000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ634-444-44-4-440000-44-4-444-40000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ644-44-44-44-44-44-44-4-44-4-4440000-444-400000000000000000000000000000000000000000000000000
χ654-44-44-44-4-24-44-422-222-2-24-44-4-222-2000000000000-22-220000000000000000000000000000000000
χ664-44-44-44-4-24-44-422-222-2-2-44-44-222-20000000000002-22-20000000000000000000000000000000000
χ674-44-44-44-4-2-44-4422-222-2-200002-2-220000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ684-44-44-44-4-2-44-4422-222-2-200002-2-2200000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ694-4-44-4-44440000-44-44-4-44000000000000000000000000000000004-4000000000000000000000000
χ704-4-44-4-44440000-44-44-4-4400000000000000000000000000000000-44000000000000000000000000
χ714-4-4-444-44-244-4-422-2-2-2224i−4i−4i4i-2-222000000000000−2i2i2i−2i0000000000000000000000000000000000
χ724-4-4-444-44-244-4-422-2-2-222−4i4i4i−4i-2-2220000000000002i−2i−2i2i0000000000000000000000000000000000
χ734-4-4-444-44-2-4-44422-2-2-222000022-2-20000004-400000000-22-22000000000000000000000000000000
χ744-4-4-444-44-2-4-44422-2-2-222000022-2-2000000-44000000002-22-2000000000000000000000000000000
χ75888-8-8-8-88-40000-444-44-440000000000000000000000000000000000000000000000000000000000
χ7688-8-8-888-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000
χ778-888-88-8-8-400004-444-4-440000000000000000000000000000000000000000000000000000000000
χ788-8-88-8-888-400004-44-444-40000000000000000000000000000000000000000000000000000000000

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