Finite Group Databasebeta

← Group #10853207

Character table — Group #10853207

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-11-1-1-1-1-1
χ411111111111111111111111111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111
χ5111111111111111111111111-1-1111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-111-1-111-1-111-1-1-111-1
χ6111111111111111111111111-1-1111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-111-1-1111-1-11
χ7111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-11111-1-1-1-1-111-1-11
χ8111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1-111-1-111111-1-111-1
χ911111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-111-111-1-1-1-11111-111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-111-1-111-1-1-1-11-1-1111
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-11-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1111-1-111-1-111-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-11-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11-1-11111-1-111111-1-1-1
χ17222222222-2-2-2-22222222000022-2-2-22222-2-20000000000000000-2-2000000002222-2-200000000000-200000
χ18222222222-2-2-2-22222222000022-2-2-22222-2-20000000000000000-2-200000000-2-2-2-22200000000000200000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-220000000000000000220000000022-2-2-2-200000000000200000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200000000000000002200000000-2-2222200000000000-200000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-222-2-222-2-2-1-1-1-1111111-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2-2-2-2-2-222-1-1-1-11111111111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1222-2-2-2-2-2-211111111-1-1111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1-22222-2-2221111-1-1-1-1111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1-2-2-22222-2-21111-1-1-1-111-1-1-1-11111000000211-1-1000000000000
χ2922-222-2-2-2222-2-22-222-2-2-222-2-20022-20000-200000000022-2-2000000000000002-2002-2000002-20000000000
χ3022-222-2-2-2222-2-22-222-2-2-222-2-20022-20000-200000000022-2-200000000000000-2200-2200000-220000000000
χ3122-222-2-2-2222-2-22-222-2-2-2-2-2220022-20000-2000000000-2-222000000000000002-2002-200000-220000000000
χ3222-222-2-2-2222-2-22-222-2-2-2-2-2220022-20000-2000000000-2-22200000000000000-2200-22000002-20000000000
χ3322-222-2-2-22-2-2222-222-2-2-2000000-2-22000020002i−2i000000002i2i−2i−2i00000000002-200-2200000002i−2i00000000
χ3422-222-2-2-22-2-2222-222-2-2-2000000-2-22000020002i−2i000000002i2i−2i−2i0000000000-22002-20000000−2i2i00000000
χ3522-222-2-2-22-2-2222-222-2-2-2000000-2-2200002000−2i2i00000000−2i−2i2i2i00000000002-200-220000000−2i2i00000000
χ3622-222-2-2-22-2-2222-222-2-2-2000000-2-2200002000−2i2i00000000−2i−2i2i2i0000000000-22002-200000002i−2i00000000
χ372-222-2-2-2222-2-22-222-22-2-22i−2i2i−2i002-2-2000020000000002i−2i2i−2i000000000000000000000000000002i−2i0002-20
χ382-222-2-2-2222-2-22-222-22-2-22i−2i2i−2i002-2-2000020000000002i−2i2i−2i00000000000000000000000000000−2i2i000-220
χ392-222-2-2-2222-2-22-222-22-2-2−2i2i−2i2i002-2-200002000000000−2i2i−2i2i000000000000000000000000000002i−2i000-220
χ402-222-2-2-2222-2-22-222-22-2-2−2i2i−2i2i002-2-200002000000000−2i2i−2i2i00000000000000000000000000000−2i2i0002-20
χ412-2-22-222-222-22-2-2-22-2-2222i−2i−2i2i002-220000-202-2002i−2i002i−2i−2i2i0000002i2i−2i−2i000000000002-200000000000000
χ422-2-22-222-222-22-2-2-22-2-2222i−2i−2i2i002-220000-20-2200−2i2i002i−2i−2i2i000000−2i−2i2i2i00000000000-2200000000000000
χ432-2-22-222-222-22-2-2-22-2-222−2i2i2i−2i002-220000-202-200−2i2i00−2i2i2i−2i000000−2i−2i2i2i000000000002-200000000000000
χ442-2-22-222-222-22-2-2-22-2-222−2i2i2i−2i002-220000-20-22002i−2i00−2i2i2i−2i0000002i2i−2i−2i00000000000-2200000000000000
χ452-2-22-222-2-12-22-211-111-1-12i−2i−2i2i00-11-1−i3−i3i3i3102-2002i−2i00−iii−i3−33−3−i3i3−i−iii33−3−30000000-11−i3i3000000000000
χ462-2-22-222-2-12-22-211-111-1-12i−2i−2i2i00-11-1−i3−i3i3i310-2200−2i2i00−iii−i3−33−3−i3i3ii−i−i−3−33300000001-1i3−i3000000000000
χ472-2-22-222-2-12-22-211-111-1-12i−2i−2i2i00-11-1i3i3−i3−i3102-2002i−2i00−iii−i−33−33i3−i3−i−iii−3−3330000000-11i3−i3000000000000
χ482-2-22-222-2-12-22-211-111-1-12i−2i−2i2i00-11-1i3i3−i3−i310-2200−2i2i00−iii−i−33−33i3−i3ii−i−i33−3−300000001-1−i3i3000000000000
χ492-2-22-222-2-12-22-211-111-1-1−2i2i2i−2i00-11-1−i3−i3i3i3102-200−2i2i00i−i−ii−33−33−i3i3ii−i−i−3−3330000000-11−i3i3000000000000
χ502-2-22-222-2-12-22-211-111-1-1−2i2i2i−2i00-11-1−i3−i3i3i310-22002i−2i00i−i−ii−33−33−i3i3−i−iii33−3−300000001-1i3−i3000000000000
χ512-2-22-222-2-12-22-211-111-1-1−2i2i2i−2i00-11-1i3i3−i3−i3102-200−2i2i00i−i−ii3−33−3i3−i3ii−i−i33−3−30000000-11i3−i3000000000000
χ522-2-22-222-2-12-22-211-111-1-1−2i2i2i−2i00-11-1i3i3−i3−i310-22002i−2i00i−i−ii3−33−3i3−i3−i−iii−3−33300000001-1−i3i3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044222-2-2-2-22-40000000000000000220000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-42222222240000000000000000-2-20000000000000000000000000000000
χ55444-4-44-4-44000044-4-4-44-400000000000000000000000000000000000000000004-40000000000000000000
χ56444-4-44-4-44000044-4-4-44-40000000000000000000000000000000000000000000-440000000000000000000
χ5744-444-4-4-4-244-4-4-22-2-222244-4-400-2-2200002000000000-2-2220000000000000000000000000000000000000
χ5844-444-4-4-4-244-4-4-22-2-2222-4-44400-2-220000200000000022-2-20000000000000000000000000000000000000
χ5944-444-4-4-4-2-4-444-22-2-222200000022-20000-20004i−4i00000000−2i−2i2i2i000000000000000000000000000000000
χ6044-444-4-4-4-2-4-444-22-2-222200000022-20000-2000−4i4i000000002i2i−2i−2i000000000000000000000000000000000
χ6144-4-4-4-444400004-4-4-44-4400004i−4i0004i−4i4i−4i000000000000000000000000000000000000000000000000000
χ6244-4-4-4-444400004-4-4-44-440000−4i4i000−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ6344-4-4-4-444-20000-2222-22-200004i−4i000−2i2i−2i2i000000000000000000006−66−6i6−i6i6−i600000000000000000000000
χ6444-4-4-4-444-20000-2222-22-200004i−4i000−2i2i−2i2i00000000000000000000−66−66−i6i6−i6i600000000000000000000000
χ6544-4-4-4-444-20000-2222-22-20000−4i4i0002i−2i2i−2i000000000000000000006−66−6−i6i6−i6i600000000000000000000000
χ6644-4-4-4-444-20000-2222-22-20000−4i4i0002i−2i2i−2i00000000000000000000−66−66i6−i6i6−i600000000000000000000000
χ674-444-4-4-444-444-4-444-44-4-4000000-4440000-400000000000000000000000000000000000000000000000000
χ684-444-4-4-44-24-4-442-2-22-2224i−4i4i−4i00-2220000-2000000000−2i2i−2i2i0000000000000000000000000000000000000
χ694-444-4-4-44-24-4-442-2-22-222−4i4i−4i4i00-2220000-20000000002i−2i2i−2i0000000000000000000000000000000000000
χ704-444-4-4-44-2-444-42-2-22-2220000002-2-2000020000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ714-444-4-4-44-2-444-42-2-22-2220000002-2-20000200000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ724-44-44-44-440000-44-44-4-44000000000000000000000−2i22i200000000000000−2i22i22i2−2i200000000000000000000000
χ734-44-44-44-440000-44-44-4-440000000000000000000002i2−2i2000000000000002i2−2i2−2i22i200000000000000000000000
χ744-44-44-44-4-200002-22-222-200000000023−23−232300000000−2i22i20000000000i6−i6−i6i6i2−i2−i2i200000000000000000000000
χ754-44-44-44-4-200002-22-222-200000000023−23−2323000000002i2−2i20000000000−i6i6i6−i6−i2i2i2−i200000000000000000000000
χ764-44-44-44-4-200002-22-222-2000000000−232323−2300000000−2i22i20000000000−i6i6i6−i6i2−i2−i2i200000000000000000000000
χ774-44-44-44-4-200002-22-222-2000000000−232323−23000000002i2−2i20000000000i6−i6−i6i6−i2i2i2−i200000000000000000000000
χ784-4-44-444-44-44-44-4-44-4-444000000-44-40000400000000000000000000000000000000000000000000000000
χ794-4-44-444-4-2-44-4422-222-2-20000002-22−2i3−2i32i32i3-2000000000000000002i3−2i30000000000000000000000000000000
χ804-4-44-444-4-2-44-4422-222-2-20000002-222i32i3−2i3−2i3-200000000000000000−2i32i30000000000000000000000000000000
χ814-4-4-444-4440000-4-4-4444-40000000000000000000000000000000000000000000000000000000000022−22000
χ824-4-4-444-4440000-4-4-4444-400000000000000000000000000000000000000000000000000000000000−2222000
χ83888-8-88-8-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000

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