Finite Group Databasebeta

← Group #10853230

Character table — Group #10853230

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
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
χ51111111111111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-11111-1-1-1
χ1011111111111111111111-1-1111111-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1111-1-1-1-1111
χ1111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-111-1-1-1-1-1-1-1111
χ1211111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-111-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-11111-1-11-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1111-1-1-1-111-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-1111-1-111-1
χ17222222222-2-2-2-22222222220000-2-22222-2-2-2000000000000-2-200000000000022-2-2-2-200000000020000000
χ18222222222-2-2-2-22222222220000-2-22222-2-2-2000000000000-2-2000000000000-2-22222000000000-20000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-220000000000002200000000000022-2-222000000000-20000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000000022000000000000-2-222-2-200000000020000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-222-2-2-2-21111-1-11111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-222-2-222-1-1-1-1111111-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-2-222-2-2-1-1-1-11111111111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2222222-2-2111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-2-2-222111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ2922-22-22-2-222-2-22-2-222-22-2002i2i−2i−2i2-200002-20000000002i2i−2i−2i0000000000000000000000000000002i−2i2-2000
χ3022-22-22-2-222-2-22-2-222-22-2002i2i−2i−2i2-200002-20000000002i2i−2i−2i000000000000000000000000000000−2i2i-22000
χ3122-22-22-2-222-2-22-2-222-22-200−2i−2i2i2i2-200002-2000000000−2i−2i2i2i0000000000000000000000000000002i−2i-22000
χ3222-22-22-2-222-2-22-2-222-22-200−2i−2i2i2i2-200002-2000000000−2i−2i2i2i000000000000000000000000000000−2i2i2-2000
χ332-2222-2-2-2222-2-22-22-22-2-2002-22-2220000-2-20000000002-22-2000000000000002-22-200000002-20000000000
χ342-2222-2-2-2222-2-22-22-22-2-2002-22-2220000-2-20000000002-22-200000000000000-22-220000000-220000000000
χ352-2222-2-2-2222-2-22-22-22-2-200-22-22220000-2-2000000000-22-22000000000000002-22-20000000-220000000000
χ362-2222-2-2-2222-2-22-22-22-2-200-22-22220000-2-2000000000-22-2200000000000000-22-2200000002-20000000000
χ372-2222-2-2-22-2-2222-22-22-2-2000000-2-200002202i−2i0000000000002i2i−2i−2i000000002-2-220000000002i−2i00000000
χ382-2222-2-2-22-2-2222-22-22-2-2000000-2-200002202i−2i0000000000002i2i−2i−2i00000000-222-2000000000−2i2i00000000
χ392-2222-2-2-22-2-2222-22-22-2-2000000-2-20000220−2i2i000000000000−2i−2i2i2i000000002-2-22000000000−2i2i00000000
χ402-2222-2-2-22-2-2222-22-22-2-2000000-2-20000220−2i2i000000000000−2i−2i2i2i00000000-222-20000000002i−2i00000000
χ412-2-22-2-22222-22-2-222-2-2-22002i−2i−2i2i2-20000-220002-2002i−2i2i−2i−2i2i0000002i2i−2i−2i00000000000002-2000000000000
χ422-2-22-2-22222-22-2-222-2-2-22002i−2i−2i2i2-20000-22000-2200−2i2i2i−2i−2i2i000000−2i−2i2i2i0000000000000-22000000000000
χ432-2-22-2-22222-22-2-222-2-2-2200−2i2i2i−2i2-20000-220002-200−2i2i−2i2i2i−2i000000−2i−2i2i2i00000000000002-2000000000000
χ442-2-22-2-22222-22-2-222-2-2-2200−2i2i2i−2i2-20000-22000-22002i−2i−2i2i2i−2i0000002i2i−2i−2i0000000000000-22000000000000
χ452-2-22-2-222-12-22-21-1-1111-1002i−2i−2i2i-1133−3−31-10002-2002i−2i−iii−i3−3−i3i3−i3i3−i−iii−i3−i3i3i300000003−3-11000000000000
χ462-2-22-2-222-12-22-21-1-1111-1002i−2i−2i2i-1133−3−31-1000-2200−2i2i−iii−i3−3−i3i3−i3i3ii−i−ii3i3−i3−i30000000−331-1000000000000
χ472-2-22-2-222-12-22-21-1-1111-1002i−2i−2i2i-11−3−3331-10002-2002i−2i−iii−i−33i3−i3i3−i3−i−iiii3i3−i3−i30000000−33-11000000000000
χ482-2-22-2-222-12-22-21-1-1111-1002i−2i−2i2i-11−3−3331-1000-2200−2i2i−iii−i−33i3−i3i3−i3ii−i−i−i3−i3i3i300000003−31-1000000000000
χ492-2-22-2-222-12-22-21-1-1111-100−2i2i2i−2i-1133−3−31-10002-200−2i2ii−i−ii3−3i3−i3i3−i3ii−i−ii3i3−i3−i300000003−3-11000000000000
χ502-2-22-2-222-12-22-21-1-1111-100−2i2i2i−2i-1133−3−31-1000-22002i−2ii−i−ii3−3i3−i3i3−i3−i−iii−i3−i3i3i30000000−331-1000000000000
χ512-2-22-2-222-12-22-21-1-1111-100−2i2i2i−2i-11−3−3331-10002-200−2i2ii−i−ii−33−i3i3−i3i3ii−i−i−i3−i3i3i30000000−33-11000000000000
χ522-2-22-2-222-12-22-21-1-1111-100−2i2i2i−2i-11−3−3331-1000-22002i−2ii−i−ii−33−i3i3−i3i3−i−iiii3i3−i3−i300000003−31-1000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022-2-2-2-222-40000000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000222222224000000000000-2-200000000000000000000000000000000000
χ55444-4-4-4-4440000-4-4-444-440000000000000000000000000000000000000000000004i−4i00000000000000000
χ56444-4-4-4-4440000-4-4-444-44000000000000000000000000000000000000000000000−4i4i00000000000000000
χ5744-44-44-4-44-444-4-4-444-44-4000000-440000-4400000000000000000000000000000000000000000000000000
χ5844-44-44-4-4-24-4-4422-2-22-22004i4i−4i−4i-220000-22000000000−2i−2i2i2i0000000000000000000000000000000000000
χ5944-44-44-4-4-24-4-4422-2-22-2200−4i−4i4i4i-220000-220000000002i2i−2i−2i0000000000000000000000000000000000000
χ6044-44-44-4-4-2-444-422-2-22-220000002-200002-200000000000000023−23−23230000000000000000000000000000000
χ6144-44-44-4-4-2-444-422-2-22-220000002-200002-2000000000000000−232323−230000000000000000000000000000000
χ6244-4-44-44-44000044-44-4-4-4000000000000000000022−22000000000000000022−2222−2200000000000000000000000
χ6344-4-44-44-44000044-44-4-4-40000000000000000000−22220000000000000000−2222−222200000000000000000000000
χ6444-4-44-44-4-20000-2-22-222200000000−2i32i3−2i32i3000000022−22000000000000i6−i6i6−i6−22−2200000000000000000000000
χ6544-4-44-44-4-20000-2-22-222200000000−2i32i3−2i32i30000000−2222000000000000−i6i6−i6i62−22−200000000000000000000000
χ6644-4-44-44-4-20000-2-22-2222000000002i3−2i32i3−2i3000000022−22000000000000−i6i6−i6i6−22−2200000000000000000000000
χ6744-4-44-44-4-20000-2-22-2222000000002i3−2i32i3−2i30000000−2222000000000000i6−i6i6−i62−22−200000000000000000000000
χ684-4444-4-4-4-244-4-4-22-22-222004-44-4-2-2000022000000000-22-220000000000000000000000000000000000000
χ694-4444-4-4-4-244-4-4-22-22-22200-44-44-2-20000220000000002-22-20000000000000000000000000000000000000
χ704-4444-4-4-4-2-4-444-22-22-222000000220000-2-204i−4i000000000000−2i−2i2i2i0000000000000000000000000000000
χ714-4444-4-4-4-2-4-444-22-22-222000000220000-2-20−4i4i0000000000002i2i−2i−2i0000000000000000000000000000000
χ724-44-4-444-440000-44-4-444-44i−4i0000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ734-44-4-444-440000-44-4-444-4−4i4i000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ744-44-4-444-4-200002-222-2-224i−4i000000−2i2i2i−2i0000000000000000000006−6−66i6−i6−i6i600000000000000000000000
χ754-44-4-444-4-200002-222-2-224i−4i000000−2i2i2i−2i000000000000000000000−666−6−i6i6i6−i600000000000000000000000
χ764-44-4-444-4-200002-222-2-22−4i4i0000002i−2i−2i2i0000000000000000000006−6−66−i6i6i6−i600000000000000000000000
χ774-44-4-444-4-200002-222-2-22−4i4i0000002i−2i−2i2i000000000000000000000−666−6i6−i6−i6i600000000000000000000000
χ784-4-44-4-4444-44-44-444-4-4-44000000-4400004-400000000000000000000000000000000000000000000000000
χ794-4-44-4-444-2-44-442-2-2222-20000002-22323−23−23-220000000000000−232300000000000000000000000000000000000
χ804-4-44-4-444-2-44-442-2-2222-20000002-2−23−232323-22000000000000023−2300000000000000000000000000000000000
χ814-4-4-444-44400004-4-4-4-444000000000000000000000000000000000000000000000000000000000000022−220
χ824-4-4-444-44400004-4-4-4-4440000000000000000000000000000000000000000000000000000000000000−22220
χ83888-8-8-8-88-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000

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