Finite Group Databasebeta

← Group #10858992

Character table — Group #10858992

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212224444488884
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
χ5111111111111111111111111-1-111-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-111-11111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-11-1-1-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-111111-1-1-1
χ911111111111111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ1011111111111111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11111-1-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-111-1-1111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1111-1-111-1-1-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-2-200000000-2-2000000000000000022-2-2-2-200000000020000000
χ18222222222-2-2-2-22222222000022-2-22222-2-2-200000000-2-20000000000000000-2-22222000000000-20000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-220000000022000000000000000022-2-222000000000-20000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200000000220000000000000000-2-222-2-200000000020000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-222-2-22211-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-222-2-211-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2222222-2-2111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
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
χ2922-222-2-2-2222-2-222-22-2-2-2000000220000-2-202-200000000000022-2-2000000002-22-200000002-20000000000
χ3022-222-2-2-2222-2-222-22-2-2-2000000220000-2-202-200000000000022-2-200000000-22-220000000-220000000000
χ3122-222-2-2-2222-2-222-22-2-2-2000000220000-2-20-22000000000000-2-222000000002-22-20000000-220000000000
χ3222-222-2-2-2222-2-222-22-2-2-2000000220000-2-20-22000000000000-2-22200000000-22-2200000002-20000000000
χ3322-222-2-2-22-2-22222-22-2-2-22i2i−2i−2i00-2-2000022000000000002i2i−2i−2i0000000000002-2-220000000002i−2i00000000
χ3422-222-2-2-22-2-22222-22-2-2-22i2i−2i−2i00-2-2000022000000000002i2i−2i−2i000000000000-222-2000000000−2i2i00000000
χ3522-222-2-2-22-2-22222-22-2-2-2−2i−2i2i2i00-2-200002200000000000−2i−2i2i2i0000000000002-2-22000000000−2i2i00000000
χ3622-222-2-2-22-2-22222-22-2-2-2−2i−2i2i2i00-2-200002200000000000−2i−2i2i2i000000000000-222-20000000002i−2i00000000
χ372-22-22-2-2222-22-2-222-2-2-222i−2i2i−2i002-200002-2000000000002i−2i2i−2i00000000000000000000000000002-22i−2i000
χ382-22-22-2-2222-22-2-222-2-2-222i−2i2i−2i002-200002-2000000000002i−2i2i−2i0000000000000000000000000000-22−2i2i000
χ392-22-22-2-2222-22-2-222-2-2-22−2i2i−2i2i002-200002-200000000000−2i2i−2i2i00000000000000000000000000002-2−2i2i000
χ402-22-22-2-2222-22-2-222-2-2-22−2i2i−2i2i002-200002-200000000000−2i2i−2i2i0000000000000000000000000000-222i−2i000
χ412-2-2-2222-22-222-2-22-2-222-22-2-2200-2200002-20002i−2i002i−2i002-2-2200002i2i−2i−2i00000000000002i−2i000000000000
χ422-2-2-2222-22-222-2-22-2-222-22-2-2200-2200002-2000−2i2i00−2i2i002-2-220000−2i−2i2i2i0000000000000−2i2i000000000000
χ432-2-2-2222-22-222-2-22-2-222-2-222-200-2200002-20002i−2i00−2i2i00-222-20000−2i−2i2i2i00000000000002i−2i000000000000
χ442-2-2-2222-22-222-2-22-2-222-2-222-200-2200002-2000−2i2i002i−2i00-222-200002i2i−2i−2i0000000000000−2i2i000000000000
χ452-2-2-2222-2-1-222-21-111-1-112-2-22001-133−3−3-110002i−2i002i−2i3−3-111-13−33−3−i−iii−i3−i3i3i30000000−i3i3−ii000000000000
χ462-2-2-2222-2-1-222-21-111-1-112-2-22001-133−3−3-11000−2i2i00−2i2i3−3-111-13−33−3ii−i−ii3i3−i3−i30000000i3−i3i−i000000000000
χ472-2-2-2222-2-1-222-21-111-1-112-2-22001-1−3−333-110002i−2i002i−2i−33-111-1−33−33−i−iiii3i3−i3−i30000000i3−i3−ii000000000000
χ482-2-2-2222-2-1-222-21-111-1-112-2-22001-1−3−333-11000−2i2i00−2i2i−33-111-1−33−33ii−i−i−i3−i3i3i30000000−i3i3i−i000000000000
χ492-2-2-2222-2-1-222-21-111-1-11-222-2001-133−3−3-110002i−2i00−2i2i3−31-1-11−33−33ii−i−ii3i3−i3−i30000000−i3i3−ii000000000000
χ502-2-2-2222-2-1-222-21-111-1-11-222-2001-133−3−3-11000−2i2i002i−2i3−31-1-11−33−33−i−iii−i3−i3i3i30000000i3−i3i−i000000000000
χ512-2-2-2222-2-1-222-21-111-1-11-222-2001-1−3−333-110002i−2i00−2i2i−331-1-113−33−3ii−i−i−i3−i3i3i30000000i3−i3−ii000000000000
χ522-2-2-2222-2-1-222-21-111-1-11-222-2001-1−3−333-11000−2i2i002i−2i−331-1-113−33−3−i−iiii3i3−i3−i30000000−i3i3i−i000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-222-40000000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-422222222400000000-2-2000000000000000000000000000000000000000
χ55444-4-44-4-4400004-44-44-4-40000000000000000000000000000000000000000000004-400000000000000000
χ56444-4-44-4-4400004-44-44-4-4000000000000000000000000000000000000000000000-4400000000000000000
χ5744-444-4-4-4-244-4-4-2-22-2222000000-2-200002204-4000000000000-2-2220000000000000000000000000000000
χ5844-444-4-4-4-244-4-4-2-22-2222000000-2-20000220-4400000000000022-2-20000000000000000000000000000000
χ5944-444-4-4-4-2-4-444-2-22-22224i4i−4i−4i00220000-2-200000000000−2i−2i2i2i00000000000000000000000000000000000
χ6044-444-4-4-4-2-4-444-2-22-2222−4i−4i4i4i00220000-2-2000000000002i2i−2i−2i00000000000000000000000000000000000
χ6144-4-4-4-444400004-4-4-4-44400004-4004-44-40000000000000000000000000000000000000000000000000000
χ6244-4-4-4-444400004-4-4-4-4440000-4400-44-440000000000000000000000000000000000000000000000000000
χ6344-4-4-4-444-20000-22222-2-200004-400-22-220000000000000000000006−66−66−66−600000000000000000000000
χ6444-4-4-4-444-20000-22222-2-200004-400-22-22000000000000000000000−66−66−66−6600000000000000000000000
χ6544-4-4-4-444-20000-22222-2-20000-44002-22-20000000000000000000006−66−6−66−6600000000000000000000000
χ6644-4-4-4-444-20000-22222-2-20000-44002-22-2000000000000000000000−66−666−66−600000000000000000000000
χ674-444-4-44-440000-4-444-44-40000000000000000000−2i22i20000000000000000−2i22i22i2−2i200000000000000000000000
χ684-444-4-44-440000-4-444-44-400000000000000000002i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000
χ694-444-4-44-4-2000022-2-22-220000000023−23−23230000000−2i22i2000000000000−i6i6i6−i6i2−i2−i2i200000000000000000000000
χ704-444-4-44-4-2000022-2-22-220000000023−23−232300000002i2−2i2000000000000i6−i6−i6i6−i2i2i2−i200000000000000000000000
χ714-444-4-44-4-2000022-2-22-2200000000−232323−230000000−2i22i2000000000000i6−i6−i6i6i2−i2−i2i200000000000000000000000
χ724-444-4-44-4-2000022-2-22-2200000000−232323−2300000002i2−2i2000000000000−i6i6i6−i6−i2i2i2−i200000000000000000000000
χ734-44-44-4-444-44-44-444-4-4-44000000-440000-4400000000000000000000000000000000000000000000000000
χ744-44-44-4-44-24-44-42-2-2222-24i−4i4i−4i00-220000-2200000000000−2i2i−2i2i00000000000000000000000000000000000
χ754-44-44-4-44-24-44-42-2-2222-2−4i4i−4i4i00-220000-22000000000002i−2i2i−2i00000000000000000000000000000000000
χ764-44-44-4-44-2-44-442-2-2222-20000002-200002-200000000000000023−23−23230000000000000000000000000000000
χ774-44-44-4-44-2-44-442-2-2222-20000002-200002-2000000000000000−232323−230000000000000000000000000000000
χ784-4-44-44-4440000-4-4-444-44000000000000000000000000000000000000000000000000000000000000022−220
χ794-4-44-44-4440000-4-4-444-440000000000000000000000000000000000000000000000000000000000000−22220
χ804-4-4-4444-444-4-44-44-4-444-40000004-40000-4400000000000000000000000000000000000000000000000000
χ814-4-4-4444-4-24-4-442-222-2-22000000-222323−23−232-2000000000−2323000000000000000000000000000000000000000
χ824-4-4-4444-4-24-4-442-222-2-22000000-22−23−2323232-200000000023−23000000000000000000000000000000000000000
χ83888-8-88-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-88-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000

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