Finite Group Databasebeta

← Group #10909531

Character table — Group #10909531

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222244444444448888888888888888888888888888812121616161616242424242424242424484848
order12222222344446666666226666121212124444444888812121212121212121212242424242424242444412121212244448888444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111111-11
χ5111111111111111111111111111111-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-1-1-11-11
χ6111111111111111111111111111111-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1
χ7111111111111111111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1111-1-11111-1-1-1
χ8111111111111111111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111
χ911111111111111111111-1-1-1-1-1-1111111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-111-1-1-11-111-1-1111-1-1
χ1011111111111111111111-1-1-1-1-1-1111111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11-11-1-111-1-1-111
χ1111111111111111111111-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-111-1-1-11-11111-1-1-1-11
χ1211111111111111111111-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-11-11-1-1-1-11111-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111-1-111-11-1-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-11111-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11-1-1111-1111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-111-11-1-1-1-1-111-111
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1111-111111-1-11-1-1
χ17222222222-2-2-2-22222222222222-2-2-2-200-200000000-2-200000000000000002200000-2-22000000000
χ18222222222-2-2-2-22222222222222-2-2-2-200-200000000-2-20000000000000000-2-20000022-2000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-20020000000022000000000000000022000002-2-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-200200000000220000000000000000-2-200000-222000000000
χ2122222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-11111111111111111002-1-1-1-1000000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100-21111000000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-22-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-21111-1-1-1-122-222-2-222-2-211-1-1-1-11111-1-1-1-1111100-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-2-222-2-222111111-1-1-1-11111-1-1-1-100-2-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-2-222-2-2-2-22211-1-1-1-111111111-1-1-1-100211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-2-2-2-22222-2-2111111-1-1-1-1-1-1-1-1111100211-1-1000000000000
χ2922-2-2-22-2222-22-222-2-2-2-2200000022-2-22i−2i0002-2002i−2i00000022-2-200002i2i−2i−2i0002i−2i00000000000000
χ3022-2-2-22-2222-22-222-2-2-2-2200000022-2-22i−2i000-2200−2i2i000000-2-2220000−2i−2i2i2i0002i−2i00000000000000
χ3122-2-2-22-2222-22-222-2-2-2-2200000022-2-2−2i2i0002-200−2i2i00000022-2-20000−2i−2i2i2i000−2i2i00000000000000
χ3222-2-2-22-2222-22-222-2-2-2-2200000022-2-2−2i2i000-22002i−2i000000-2-22200002i2i−2i−2i000−2i2i00000000000000
χ3322-2-2-22-22-12-22-2-1-11111-100−i3−i3i3i3-1-1112i−2i0002-2002i−2i−i3i3−i3−i3i3i3-1-11133−3−3−i−iii000−ii3−3000000000000
χ3422-2-2-22-22-12-22-2-1-11111-100−i3−i3i3i3-1-1112i−2i000-2200−2i2i−i3i3i3i3−i3−i311-1-1−3−333ii−i−i000−ii3−3000000000000
χ3522-2-2-22-22-12-22-2-1-11111-100−i3−i3i3i3-1-111−2i2i0002-200−2i2i−i3i3−i3−i3i3i3-1-111−3−333ii−i−i000i−i−33000000000000
χ3622-2-2-22-22-12-22-2-1-11111-100−i3−i3i3i3-1-111−2i2i000-22002i−2i−i3i3i3i3−i3−i311-1-133−3−3−i−iii000i−i−33000000000000
χ3722-2-2-22-22-12-22-2-1-11111-100i3i3−i3−i3-1-1112i−2i0002-2002i−2ii3−i3i3i3−i3−i3-1-111−3−333−i−iii000−ii−33000000000000
χ3822-2-2-22-22-12-22-2-1-11111-100i3i3−i3−i3-1-1112i−2i000-2200−2i2ii3−i3−i3−i3i3i311-1-133−3−3ii−i−i000−ii−33000000000000
χ3922-2-2-22-22-12-22-2-1-11111-100i3i3−i3−i3-1-111−2i2i0002-200−2i2ii3−i3i3i3−i3−i3-1-11133−3−3ii−i−i000i−i3−3000000000000
χ4022-2-2-22-22-12-22-2-1-11111-100i3i3−i3−i3-1-111−2i2i000-22002i−2ii3−i3−i3−i3i3i311-1-1−3−333−i−iii000i−i3−3000000000000
χ412-22-2-2-2222-2-222-2-22-22-220000002-22-20002-2000000002-22-200000000000000000000002-2002-2000
χ422-22-2-2-2222-2-222-2-22-22-220000002-22-20002-2000000002-22-20000000000000000000000-2200-22000
χ432-22-2-2-2222-2-222-2-22-22-220000002-22-2000-2200000000-22-2200000000000000000000002-200-22000
χ442-22-2-2-2222-2-222-2-22-22-220000002-22-2000-2200000000-22-220000000000000000000000-22002-2000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244-2-2-2-2222200-4000000002200000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-42222222200400000000-2-200000000000000000000000000000000000
χ47444-44-4-4-4400004-4-4-444-44-44-44-40000000000000000000000000000000000000000000000000000
χ48444-44-4-4-4400004-4-4-444-4-44-44-440000000000000000000000000000000000000000000000000000
χ49444-44-4-4-4-20000-2222-2-224-4-22-2200000000000000000000000006−66−66−66−60000000000000000000
χ50444-44-4-4-4-20000-2222-2-224-4-22-220000000000000000000000000−66−66−66−660000000000000000000
χ51444-44-4-4-4-20000-2222-2-22-442-22-200000000000000000000000006−66−6−66−660000000000000000000
χ52444-44-4-4-4-20000-2222-2-22-442-22-20000000000000000000000000−66−666−66−60000000000000000000
χ5344-44-4-44-4400004-444-4-4-40000000000000000022−2200000000000022−22−222200000000000000000000000
χ5444-44-4-44-4400004-444-4-4-400000000000000000−2222000000000000−222222−2200000000000000000000000
χ5544-44-4-44-4-20000-22-2-222200−2i32i32i3−2i30000000000022−22000000000000−222−2−i6i6i6−i60000000000000000000
χ5644-44-4-44-4-20000-22-2-222200−2i32i32i3−2i300000000000−22220000000000002−2−22i6−i6−i6i60000000000000000000
χ5744-44-4-44-4-20000-22-2-2222002i3−2i3−2i32i30000000000022−22000000000000−222−2i6−i6−i6i60000000000000000000
χ5844-44-4-44-4-20000-22-2-2222002i3−2i3−2i32i300000000000−22220000000000002−2−22−i6i6i6−i60000000000000000000
χ5944-4-4-44-444-44-4444-4-4-4-44000000-4-444000000000000000000000000000000000000000000000000
χ6044-4-4-44-44-2-44-44-2-22222-200−2i3−2i32i32i322-2-2000000000002i3−2i300000000000000000000000000000000000
χ6144-4-4-44-44-2-44-44-2-22222-2002i32i3−2i3−2i322-2-200000000000−2i32i300000000000000000000000000000000000
χ624-444-44-4-440000-44-444-4-400000000000000000000000000000000000000000000000000022−2200000
χ634-444-44-4-440000-44-444-4-4000000000000000000000000000000000000000000000000000−222200000
χ644-44-4-4-444444-4-4-4-44-44-44000000-44-44000000000000000000000000000000000000000000000000
χ654-44-4-4-444-244-4-422-22-22-20000002-22-200000000000000000−2i32i3−2i32i3000000000000000000000000000
χ664-44-4-4-444-244-4-422-22-22-20000002-22-2000000000000000002i3−2i32i3−2i3000000000000000000000000000
χ674-44-4-4-444-2-4-44422-22-22-2000000-22-220004-400000000-22-220000000000000000000000000000000
χ684-44-4-4-444-2-4-44422-22-22-2000000-22-22000-44000000002-22-20000000000000000000000000000000
χ694-4-444-4-4444-4-44-4-4-44-444000000-444-4000000000000000000000000000000000000000000000000
χ704-4-444-4-444-444-4-4-4-44-4440000004-4-44000000000000000000000000000000000000000000000000
χ714-4-444-4-44-24-4-44222-22-2-20000002-2-2200000000000000000−2i32i32i3−2i3000000000000000000000000000
χ724-4-444-4-44-24-4-44222-22-2-20000002-2-22000000000000000002i3−2i3−2i32i3000000000000000000000000000
χ734-4-444-4-44-2-444-4222-22-2-2000000-222-20000000000000−2i32i32i3−2i30000000000000000000000000000000
χ744-4-444-4-44-2-444-4222-22-2-2000000-222-200000000000002i3−2i3−2i32i30000000000000000000000000000000
χ754-4-4-4444-440000-444-4-44-40000000000000000000000000000000000000004i−4i00000000000000000
χ764-4-4-4444-440000-444-4-44-4000000000000000000000000000000000000000−4i4i00000000000000000
χ778-888-88-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000
χ788-8-8-8888-8-400004-4-444-440000000000000000000000000000000000000000000000000000000000

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