Finite Group Databasebeta

← Group #10827621

Character table — Group #10827621

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424222244412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ911111111111111111111-1-11111-1-1-1-11111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-11111-1-1-111-1-111-1
χ1011111111111111111111-1-11111-1-1-1-11111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-111-1-11
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-111-1-1-1-1-111-1-11
χ1211111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111-1-1-1-111111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-111-1-111-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-11111-1-11-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-1-1-111-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-111-1-111111-1-1-1
χ17222222222-2-2-2-222222222200002222-2-2-2-2-200000000-2-2000000000000000022-2-2-2-200000000020000000
χ18222222222-2-2-2-222222222200002222-2-2-2-2-200000000-2-20000000000000000-2-22222000000000-20000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-22000000002200000000000000002222-2-2000000000-20000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000220000000000000000-2-2-2-22200000000020000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-222-2-22211-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-222-2-211-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2222222-2-2111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-222-2-2-2-222111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ2922-22-2-2-2222-22-22-2-2-22-22002i2i−2i−2i000022-2-2000000000002i2i−2i−2i00000000000000000000000000002-2002i−2i0
χ3022-22-2-2-2222-22-22-2-2-22-22002i2i−2i−2i000022-2-2000000000002i2i−2i−2i0000000000000000000000000000-2200−2i2i0
χ3122-22-2-2-2222-22-22-2-2-22-2200−2i−2i2i2i000022-2-200000000000−2i−2i2i2i00000000000000000000000000002-200−2i2i0
χ3222-22-2-2-2222-22-22-2-2-22-2200−2i−2i2i2i000022-2-200000000000−2i−2i2i2i0000000000000000000000000000-22002i−2i0
χ332-22-22-2-22222-2-2-222-2-2-22002i−2i2i−2i00002-22-20002-2002i−2i002i−2i2i−2i00002i2i−2i−2i00000000000002-2000000000000
χ342-22-22-2-22222-2-2-222-2-2-22002i−2i2i−2i00002-22-2000-2200−2i2i002i−2i2i−2i0000−2i−2i2i2i0000000000000-22000000000000
χ352-22-22-2-22222-2-2-222-2-2-2200−2i2i−2i2i00002-22-20002-200−2i2i00−2i2i−2i2i0000−2i−2i2i2i00000000000002-2000000000000
χ362-22-22-2-22222-2-2-222-2-2-2200−2i2i−2i2i00002-22-2000-22002i−2i00−2i2i−2i2i00002i2i−2i−2i0000000000000-22000000000000
χ372-22-22-2-22-122-2-21-1-1111-1002i−2i2i−2i33−3−3-11-110002-2002i−2i3−3−ii−ii−i3−i3i3i3−i−iii−i3−i3i3i300000003−3-11000000000000
χ382-22-22-2-22-122-2-21-1-1111-1002i−2i2i−2i33−3−3-11-11000-2200−2i2i3−3−ii−ii−i3−i3i3i3ii−i−ii3i3−i3−i30000000−331-1000000000000
χ392-22-22-2-22-122-2-21-1-1111-1002i−2i2i−2i−3−333-11-110002-2002i−2i−33−ii−iii3i3−i3−i3−i−iiii3i3−i3−i30000000−33-11000000000000
χ402-22-22-2-22-122-2-21-1-1111-1002i−2i2i−2i−3−333-11-11000-2200−2i2i−33−ii−iii3i3−i3−i3ii−i−i−i3−i3i3i300000003−31-1000000000000
χ412-22-22-2-22-122-2-21-1-1111-100−2i2i−2i2i33−3−3-11-110002-200−2i2i3−3i−ii−ii3i3−i3−i3ii−i−ii3i3−i3−i300000003−3-11000000000000
χ422-22-22-2-22-122-2-21-1-1111-100−2i2i−2i2i33−3−3-11-11000-22002i−2i3−3i−ii−ii3i3−i3−i3−i−iii−i3−i3i3i30000000−331-1000000000000
χ432-22-22-2-22-122-2-21-1-1111-100−2i2i−2i2i−3−333-11-110002-200−2i2i−33i−ii−i−i3−i3i3i3ii−i−i−i3−i3i3i30000000−33-11000000000000
χ442-22-22-2-22-122-2-21-1-1111-100−2i2i−2i2i−3−333-11-11000-22002i−2i−33i−ii−i−i3−i3i3i3−i−iiii3i3−i3−i300000003−31-1000000000000
χ452-2-2-2-222222-2-22-2-2-22-222002-2-2200002-2-22000000000002-2-220000000000002-2002-2000002-20000000000
χ462-2-2-2-222222-2-22-2-2-22-222002-2-2200002-2-22000000000002-2-22000000000000-2200-2200000-220000000000
χ472-2-2-2-222222-2-22-2-2-22-22200-222-200002-2-2200000000000-222-20000000000002-2002-200000-220000000000
χ482-2-2-2-222222-2-22-2-2-22-22200-222-200002-2-2200000000000-222-2000000000000-2200-22000002-20000000000
χ492-2-2-2-22222-222-2-2-2-22-2220000000000-222-202-20000000000002-22-2000000002-200-2200000002-200000000
χ502-2-2-2-22222-222-2-2-2-22-2220000000000-222-202-20000000000002-22-200000000-22002-20000000-2200000000
χ512-2-2-2-22222-222-2-2-2-22-2220000000000-222-20-22000000000000-22-22000000002-200-220000000-2200000000
χ522-2-2-2-22222-222-2-2-2-22-2220000000000-222-20-22000000000000-22-2200000000-22002-200000002-200000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-22222-40000000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222400000000-2-2000000000000000000000000000000000000000
χ55444-4-4-44-44000044-4-4-44-400000000000000000000000000000000000000000004-40000000000000000000
χ56444-4-4-44-44000044-4-4-44-40000000000000000000000000000000000000000000-440000000000000000000
χ5744-44-4-4-444-44-444-4-4-44-440000000000-4-44400000000000000000000000000000000000000000000000000
χ5844-44-4-4-44-24-44-4-2222-22-2004i4i−4i−4i0000-2-22200000000000−2i−2i2i2i00000000000000000000000000000000000
χ5944-44-4-4-44-24-44-4-2222-22-200−4i−4i4i4i0000-2-222000000000002i2i−2i−2i00000000000000000000000000000000000
χ6044-44-4-4-44-2-44-44-2222-22-2000000000022-2-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ6144-44-4-4-44-2-44-44-2222-22-2000000000022-2-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ6244-4-444-4-4400004-444-4-4-4000000000000000000022−22000000000000000022−2222−2200000000000000000000000
χ6344-4-444-4-4400004-444-4-4-40000000000000000000−22220000000000000000−2222−222200000000000000000000000
χ6444-4-444-4-4-20000-22-2-2222000000−2i32i3−2i32i300000000022−22000000000000i6−i6i6−i6−22−2200000000000000000000000
χ6544-4-444-4-4-20000-22-2-2222000000−2i32i3−2i32i3000000000−2222000000000000−i6i6−i6i62−22−200000000000000000000000
χ6644-4-444-4-4-20000-22-2-22220000002i3−2i32i3−2i300000000022−22000000000000−i6i6−i6i6−22−2200000000000000000000000
χ6744-4-444-4-4-20000-22-2-22220000002i3−2i32i3−2i3000000000−2222000000000000i6−i6i6−i62−22−200000000000000000000000
χ684-444-44-4-440000-44-444-4-40000000000000000000000000000000000000000000000000000000000022−22000
χ694-444-44-4-440000-44-444-4-400000000000000000000000000000000000000000000000000000000000−2222000
χ704-44-44-4-444-4-444-444-4-4-440000000000-44-4400000000000000000000000000000000000000000000000000
χ714-44-44-4-44-2-4-4442-2-2222-20000002323−23−232-22-2000000000−2323000000000000000000000000000000000000000
χ724-44-44-4-44-2-4-4442-2-2222-2000000−23−2323232-22-200000000023−23000000000000000000000000000000000000000
χ734-4-444-44-440000-4-44-444-44i−4i00004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ744-4-444-44-440000-4-44-444-4−4i4i0000−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ754-4-444-44-4-2000022-22-2-224i−4i0000−2i2i2i−2i000000000000000000000006−6−66i6−i6−i6i600000000000000000000000
χ764-4-444-44-4-2000022-22-2-224i−4i0000−2i2i2i−2i00000000000000000000000−666−6−i6i6i6−i600000000000000000000000
χ774-4-444-44-4-2000022-22-2-22−4i4i00002i−2i−2i2i000000000000000000000006−6−66−i6i6i6−i600000000000000000000000
χ784-4-444-44-4-2000022-22-2-22−4i4i00002i−2i−2i2i00000000000000000000000−666−6i6−i6−i6i600000000000000000000000
χ794-4-4-4-4444-24-4-44222-22-2-2004-4-440000-222-200000000000-222-200000000000000000000000000000000000
χ804-4-4-4-4444-24-4-44222-22-2-200-444-40000-222-2000000000002-2-2200000000000000000000000000000000000
χ814-4-4-4-4444-2-444-4222-22-2-200000000002-2-2204-4000000000000-22-220000000000000000000000000000000
χ824-4-4-4-4444-2-444-4222-22-2-200000000002-2-220-440000000000002-22-20000000000000000000000000000000
χ83888-8-8-88-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000

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