Finite Group Databasebeta

← Group #10859035

Character table — Group #10859035

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
χ3111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ4111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1111111-1
χ71111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ911111111111111111111-1-11111111-1-1-1-11-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-111-1-1-111-1-111-1
χ1011111111111111111111-1-11111111-1-1-1-11-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1111-1-111-1-11
χ1111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-111-1-1-1-1-11111-1-11
χ1211111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1-11111111-1-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-11111-1-1-111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-1111-1-1111
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-111-1-111-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-11111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-22222-20000-20000-2-200000000000000002222-2-2000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-22222-20000-20000-2-20000000000000000-2-2-2-22200000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200002000022000000000000000022-2-2-2-200000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000020000220000000000000000-2-22222000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-222222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-222-222-2-211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-12222-2-2-222111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-2-2-222-2-2111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ29222-2-2-22-2222-2-22-22-22-2-200000022-20000-22-2000000000000022-2-2000000002-2002-200000002-200000000
χ30222-2-2-22-2222-2-22-22-22-2-200000022-20000-22-2000000000000022-2-200000000-2200-220000000-2200000000
χ31222-2-2-22-2222-2-22-22-22-2-200000022-20000-2-220000000000000-2-222000000002-2002-20000000-2200000000
χ32222-2-2-22-2222-2-22-22-22-2-200000022-20000-2-220000000000000-2-22200000000-2200-2200000002-200000000
χ33222-2-2-22-22-2-2222-22-22-2-2002i2i−2i−2i-2-2200002000000000002i2i−2i−2i0000000000002-200-2200000000002i−2i00000
χ34222-2-2-22-22-2-2222-22-22-2-2002i2i−2i−2i-2-2200002000000000002i2i−2i−2i000000000000-22002-20000000000−2i2i00000
χ35222-2-2-22-22-2-2222-22-22-2-200−2i−2i2i2i-2-220000200000000000−2i−2i2i2i0000000000002-200-220000000000−2i2i00000
χ36222-2-2-22-22-2-2222-22-22-2-200−2i−2i2i2i-2-220000200000000000−2i−2i2i2i000000000000-22002-200000000002i−2i00000
χ372-2-22-2-22222-22-2-222-2-22-2002-22-22-220000-2000000000002-22-2000000000000000000000002i−2i00000002i−2i0
χ382-2-22-2-22222-22-2-222-2-22-2002-22-22-220000-2000000000002-22-200000000000000000000000−2i2i0000000−2i2i0
χ392-2-22-2-22222-22-2-222-2-22-200-22-222-220000-200000000000-22-22000000000000000000000002i−2i0000000−2i2i0
χ402-2-22-2-22222-22-2-222-2-22-200-22-222-220000-200000000000-22-2200000000000000000000000−2i2i00000002i−2i0
χ412-2-2-2222-22-222-2-2-222-2-22002i−2i−2i2i-2220000-2002-202i−2i00002i−2i−2i2i00002i2i−2i−2i000000000002-200000000000000
χ422-2-2-2222-22-222-2-2-222-2-22002i−2i−2i2i-2220000-200-220−2i2i00002i−2i−2i2i0000−2i−2i2i2i00000000000-2200000000000000
χ432-2-2-2222-22-222-2-2-222-2-2200−2i2i2i−2i-2220000-2002-20−2i2i0000−2i2i2i−2i0000−2i−2i2i2i000000000002-200000000000000
χ442-2-2-2222-22-222-2-2-222-2-2200−2i2i2i−2i-2220000-200-2202i−2i0000−2i2i2i−2i00002i2i−2i−2i00000000000-2200000000000000
χ452-2-2-2222-2-1-222-211-1-111-1002i−2i−2i2i1-1-1−i3−i3i3i31002-202i−2i00−i3i3−iii−i3−33−3−i−iii33−3−30000000-11−i3i3000000000000
χ462-2-2-2222-2-1-222-211-1-111-1002i−2i−2i2i1-1-1−i3−i3i3i3100-220−2i2i00−i3i3−iii−i3−33−3ii−i−i−3−33300000001-1i3−i3000000000000
χ472-2-2-2222-2-1-222-211-1-111-1002i−2i−2i2i1-1-1i3i3−i3−i31002-202i−2i00i3−i3−iii−i−33−33−i−iii−3−3330000000-11i3−i3000000000000
χ482-2-2-2222-2-1-222-211-1-111-1002i−2i−2i2i1-1-1i3i3−i3−i3100-220−2i2i00i3−i3−iii−i−33−33ii−i−i33−3−300000001-1−i3i3000000000000
χ492-2-2-2222-2-1-222-211-1-111-100−2i2i2i−2i1-1-1−i3−i3i3i31002-20−2i2i00−i3i3i−i−ii−33−33ii−i−i−3−3330000000-11−i3i3000000000000
χ502-2-2-2222-2-1-222-211-1-111-100−2i2i2i−2i1-1-1−i3−i3i3i3100-2202i−2i00−i3i3i−i−ii−33−33−i−iii33−3−300000001-1i3−i3000000000000
χ512-2-2-2222-2-1-222-211-1-111-100−2i2i2i−2i1-1-1i3i3−i3−i31002-20−2i2i00i3−i3i−i−ii3−33−3ii−i−i33−3−30000000-11i3−i3000000000000
χ522-2-2-2222-2-1-222-211-1-111-100−2i2i2i−2i1-1-1i3i3−i3−i3100-2202i−2i00i3−i3i−i−ii3−33−3−i−iii−3−33300000001-1−i3i3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000222-2-2-2-220000-4000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222000040000-2-2000000000000000000000000000000000000000
χ55444-4-4-44-4-244-4-4-22-22-222000000-2-22000024-40000000000000-2-2220000000000000000000000000000000
χ56444-4-4-44-4-244-4-4-22-22-222000000-2-2200002-44000000000000022-2-20000000000000000000000000000000
χ57444-4-4-44-4-2-4-444-22-22-222004i4i−4i−4i22-20000-200000000000−2i−2i2i2i00000000000000000000000000000000000
χ58444-4-4-44-4-2-4-444-22-22-22200−4i−4i4i4i22-20000-2000000000002i2i−2i−2i00000000000000000000000000000000000
χ5944-444-4-4-44000044-4-4-4-444-400000004-44-4000000000000000000000000000000000000000000000000000
χ6044-444-4-4-44000044-4-4-4-44-440000000-44-44000000000000000000000000000000000000000000000000000
χ6144-444-4-4-4-20000-2-22222-24-40000000-22-22000000000000000000006−66−66−66−600000000000000000000000
χ6244-444-4-4-4-20000-2-22222-24-40000000-22-2200000000000000000000−66−66−66−6600000000000000000000000
χ6344-444-4-4-4-20000-2-22222-2-4400000002-22-2000000000000000000006−66−6−66−6600000000000000000000000
χ6444-444-4-4-4-20000-2-22222-2-4400000002-22-200000000000000000000−66−666−66−600000000000000000000000
χ6544-4-4-44-44400004-4-44-44-400000000000000000000000000000000000000000004i−4i0000000000000000000
χ6644-4-4-44-44400004-4-44-44-40000000000000000000000000000000000000000000−4i4i0000000000000000000
χ674-444-44-4-440000-44-444-4-40000000000000000000000000000000000000000000000000000000000022−22000
χ684-444-44-4-440000-44-444-4-400000000000000000000000000000000000000000000000000000000000−2222000
χ694-44-44-4-4440000-4-4-4-444400000000000000000000022−220000000000000022−22−222200000000000000000000000
χ704-44-44-4-4440000-4-4-4-4444000000000000000000000−222200000000000000−222222−2200000000000000000000000
χ714-44-44-4-44-200002222-2-2-2000000000−2i32i32i3−2i30000000022−220000000000−i6i6i6−i6−222−200000000000000000000000
χ724-44-44-4-44-200002222-2-2-2000000000−2i32i32i3−2i300000000−22220000000000i6−i6−i6i62−2−2200000000000000000000000
χ734-44-44-4-44-200002222-2-2-20000000002i3−2i3−2i32i30000000022−220000000000i6−i6−i6i6−222−200000000000000000000000
χ744-44-44-4-44-200002222-2-2-20000000002i3−2i3−2i32i300000000−22220000000000−i6i6i6−i62−2−2200000000000000000000000
χ754-4-44-4-4444-44-44-444-4-44-4000000-44-40000400000000000000000000000000000000000000000000000000
χ764-4-44-4-444-24-44-42-2-222-22004-44-4-22-20000200000000000-22-2200000000000000000000000000000000000
χ774-4-44-4-444-24-44-42-2-222-2200-44-44-22-200002000000000002-22-200000000000000000000000000000000000
χ784-4-44-4-444-2-44-442-2-222-220000002-220000-200000000000000023−23−23230000000000000000000000000000000
χ794-4-44-4-444-2-44-442-2-222-220000002-220000-2000000000000000−232323−230000000000000000000000000000000
χ804-4-4-4444-444-4-44-4-444-4-440000004-4-40000400000000000000000000000000000000000000000000000000
χ814-4-4-4444-4-24-4-4422-2-222-2000000-222−2i3−2i32i32i3-20000000002i3−2i3000000000000000000000000000000000000000
χ824-4-4-4444-4-24-4-4422-2-222-2000000-2222i32i3−2i3−2i3-2000000000−2i32i3000000000000000000000000000000000000000
χ8388-8-8-88-88-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000

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