Finite Group Databasebeta

← Group #10868270

Character table — Group #10868270

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121216161616161616161616242424242424242424242424
order122222223444466666664444121212124444888812121212242424242424242444444444441212121212121212244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1111111
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-111-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-111-1-1-1-1
χ911111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1111-1-1-1-1111-111-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-111-11-1-1111111-1-1
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111-11111-1-1-1-11-1-1-1-1-11111-1-1
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-11111-1-1-1-1-111111-1-1-1-111
χ1311111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-1-11111-1-1-1111-1-1-1-111-1-1
χ1411111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-11-1-1-11111-1-111
χ1511111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-11-1-1-1-11111-11-1-1-1-111-1-111
χ1611111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-1-1-111111-11111-1-111-1-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2-20000000022-2-200000000000022220000000000-2-20000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-20000000022-2-2000000000000-2-2-2-20000000000220000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-200000000-2-22200000000000022-2-200000000002-20000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-200000000-2-222000000000000-2-2220000000000-220000000000
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-2-2-2-2-1-1-1-11111111100000000-2-2-1-111-1-111000000000000
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
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111000000002211-1-111-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-222-2-21111-1-1-1-1111100000000-22-1-11111-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-2-22211111111-1-1-1-1000000002-2-1-1-1-11111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22222-2-21111-1-1-1-11111000000002-211-1-1-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-222-2-22211111111-1-1-1-100000000-221111-1-1-1-1000000000000
χ2922-2-2-2-22222-2-222-2-22-2-222i−2i2i−2i2-22-22i−2i2-200002i−2i2i−2i0000000000000000002i−2i002-200000000000000
χ3022-2-2-2-22222-2-222-2-22-2-222i−2i2i−2i2-22-2−2i2i-2200002i−2i2i−2i000000000000000000−2i2i00-2200000000000000
χ3122-2-2-2-22222-2-222-2-22-2-22−2i2i−2i2i2-22-22i−2i-220000−2i2i−2i2i0000000000000000002i−2i00-2200000000000000
χ3222-2-2-2-22222-2-222-2-22-2-22−2i2i−2i2i2-22-2−2i2i2-20000−2i2i−2i2i000000000000000000−2i2i002-200000000000000
χ3322-2-2-2-2222-222-22-2-22-2-222i−2i−2i2i-22-22000000002i−2i−2i2i000000002i2i−2i−2i0000000000000000002-2000000
χ3422-2-2-2-2222-222-22-2-22-2-222i−2i−2i2i-22-22000000002i−2i−2i2i00000000−2i−2i2i2i000000000000000000-22000000
χ3522-2-2-2-2222-222-22-2-22-2-22−2i2i2i−2i-22-2200000000−2i2i2i−2i000000002i2i−2i−2i000000000000000000-22000000
χ3622-2-2-2-2222-222-22-2-22-2-22−2i2i2i−2i-22-2200000000−2i2i2i−2i00000000−2i−2i2i2i0000000000000000002-2000000
χ3722-2-2-2-222-12-2-22-111-111-12i−2i2i−2i-11-112i−2i2-20000−ii−ii33−3−3−i3−i3i3i30000000000−ii3−3-11−i3i3000000000000
χ3822-2-2-2-222-12-2-22-111-111-12i−2i2i−2i-11-112i−2i2-20000−ii−ii−3−333i3i3−i3−i30000000000−ii−33-11i3−i3000000000000
χ3922-2-2-2-222-12-2-22-111-111-12i−2i2i−2i-11-11−2i2i-220000−ii−ii33−3−3−i3−i3i3i30000000000i−i−331-1i3−i3000000000000
χ4022-2-2-2-222-12-2-22-111-111-12i−2i2i−2i-11-11−2i2i-220000−ii−ii−3−333i3i3−i3−i30000000000i−i3−31-1−i3i3000000000000
χ4122-2-2-2-222-12-2-22-111-111-1−2i2i−2i2i-11-112i−2i-220000i−ii−i33−3−3i3i3−i3−i30000000000−ii−331-1−i3i3000000000000
χ4222-2-2-2-222-12-2-22-111-111-1−2i2i−2i2i-11-112i−2i-220000i−ii−i−3−333−i3−i3i3i30000000000−ii3−31-1i3−i3000000000000
χ4322-2-2-2-222-12-2-22-111-111-1−2i2i−2i2i-11-11−2i2i2-20000i−ii−i33−3−3i3i3−i3−i30000000000i−i3−3-11i3−i3000000000000
χ4422-2-2-2-222-12-2-22-111-111-1−2i2i−2i2i-11-11−2i2i2-20000i−ii−i−3−333−i3−i3i3i30000000000i−i−33-11−i3i3000000000000
χ452-22-22-22-222-22-2-2-2-2222-2000022-2-200002i−2i0000002i−2i2i−2i00002-22-200000000000000002i−2i00000000
χ462-22-22-22-222-22-2-2-2-2222-2000022-2-200002i−2i0000002i−2i2i−2i0000-22-220000000000000000−2i2i00000000
χ472-22-22-22-222-22-2-2-2-2222-2000022-2-20000−2i2i000000−2i2i−2i2i00002-22-20000000000000000−2i2i00000000
χ482-22-22-22-222-22-2-2-2-2222-2000022-2-20000−2i2i000000−2i2i−2i2i0000-22-2200000000000000002i−2i00000000
χ492-2-22-222-22-2-222-2222-2-2-20000-222-20000002-2000000002-22-22i−2i−2i2i000000000000000000002i−2i0000
χ502-2-22-222-22-2-222-2222-2-2-20000-222-20000002-2000000002-22-2−2i2i2i−2i00000000000000000000−2i2i0000
χ512-2-22-222-22-2-222-2222-2-2-20000-222-2000000-2200000000-22-222i−2i−2i2i00000000000000000000−2i2i0000
χ522-2-22-222-22-2-222-2222-2-2-20000-222-2000000-2200000000-22-22−2i2i2i−2i000000000000000000002i−2i0000
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
χ55444-4-44-4-44000044-4-44-4-40000000000000000000000000000000000000000000000000000000022−22
χ56444-4-44-4-44000044-4-44-4-400000000000000000000000000000000000000000000000000000000−2222
χ5744-444-4-4-4400004-44-4-44-400000000000000000000000000000000000000000000000000000022−2200
χ5844-444-4-4-4400004-44-4-44-4000000000000000000000000000000000000000000000000000000−222200
χ5944-4-4-4-444-2-444-4-222-222-24i−4i−4i4i2-22-200000000−2i2i2i−2i00000000000000000000000000000000000000
χ6044-4-4-4-444-2-444-4-222-222-2−4i4i4i−4i2-22-2000000002i−2i−2i2i00000000000000000000000000000000000000
χ614-444-4-4-4440000-4-44-44-4400000000000000000000000000000000004i−4i0000000000000000000000
χ624-444-4-4-4440000-4-44-44-440000000000000000000000000000000000−4i4i0000000000000000000000
χ634-44-44-44-44-44-44-4-4-4444-40000-4-44400000000000000000000000000000000000000000000000000
χ644-44-44-44-4-24-44-4222-2-2-220000-2-22200004i−4i000000−2i2i−2i2i0000000000000000000000000000000000
χ654-44-44-44-4-24-44-4222-2-2-220000-2-2220000−4i4i0000002i−2i2i−2i0000000000000000000000000000000000
χ664-44-44-44-4-2-44-44222-2-2-22000022-2-20000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ674-44-44-44-4-2-44-44222-2-2-22000022-2-200000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ684-4-44-444-4444-4-4-4444-4-4-400004-4-4400000000000000000000000000000000000000000000000000
χ694-4-44-444-4-244-4-42-2-2-22220000-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ704-4-44-444-4-244-4-42-2-2-22220000-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ714-4-44-444-4-2-4-4442-2-2-222200002-2-220000004-400000000-22-22000000000000000000000000000000
χ724-4-44-444-4-2-4-4442-2-2-222200002-2-22000000-44000000002-22-2000000000000000000000000000000
χ734-4-4-444-4440000-44-4-4-444000000000000000000000000000000004-4000000000000000000000000
χ744-4-4-444-4440000-44-4-4-44400000000000000000000000000000000-44000000000000000000000000
χ75888-8-88-8-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000
χ7688-888-8-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000
χ778-888-8-8-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000
χ788-8-8-888-88-400004-4444-4-40000000000000000000000000000000000000000000000000000000000

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