Finite Group Databasebeta

← Group #10868238

Character table — Group #10868238

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212121212121616161624242424242424244848
order122222223444466666664444121212121212121244444444888812121212121212121212242424242424242444444444121212122224888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ511111111111111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-1-1-111
χ611111111111111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-111111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-111
χ911111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1111-1-111-11
χ1011111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-11-1-1-111-1-11-1
χ1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-111111-1-11-1
χ1211111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-11-1-1-1-1-111-11
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1111-1-1-11
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1-1-1111-1
χ1511111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-111-1-1-11-1-1111-1
χ1611111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-111111-111-1-1-11
χ17222222222-2-2-2-2222222222-2-2-2-22222-2-2000000000000-2-2000000000000000022-2-200000000200-2000000
χ18222222222-2-2-2-2222222222-2-2-2-22222-2-2000000000000-2-20000000000000000-2-22200000000-2002000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000220000000000000000222200000000-200-2000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2-2-2000000002002000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1111111111111111100000000-1-1-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000011110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000000011110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-12222-2-2-2-2-2-22211-1-1-1-11111-1-1-1-1111100000000-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-2-2-22222-2-2111111-1-1-1-11111-1-1-1-100000000-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-22222-2-222-2-211-1-1-1-111111111-1-1-1-10000000011-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-2-2-22222-2-222111111-1-1-1-1-1-1-1-111110000000011-1-10000000000
χ2922-2-22-22-222-2-222-22-2-2-222i−2i2i−2i2-22i2i−2i−2i2-22i−2i002-20000002i−2i0000000000000000000000002i−2i2-20000000000
χ3022-2-22-22-222-2-222-22-2-2-222i−2i2i−2i2-22i2i−2i−2i2-2−2i2i00-220000002i−2i000000000000000000000000−2i2i-220000000000
χ3122-2-22-22-222-2-222-22-2-2-22−2i2i−2i2i2-2−2i−2i2i2i2-22i−2i00-22000000−2i2i0000000000000000000000002i−2i-220000000000
χ3222-2-22-22-222-2-222-22-2-2-22−2i2i−2i2i2-2−2i−2i2i2i2-2−2i2i002-2000000−2i2i000000000000000000000000−2i2i2-20000000000
χ3322-2-22-22-22-222-22-22-2-2-222i−2i−2i2i-222i2i−2i−2i-22000000000000−2i2i000000000000000000002i2i−2i−2i000002-20000000
χ3422-2-22-22-22-222-22-22-2-2-222i−2i−2i2i-222i2i−2i−2i-22000000000000−2i2i00000000000000000000−2i−2i2i2i00000-220000000
χ3522-2-22-22-22-222-22-22-2-2-22−2i2i2i−2i-22−2i−2i2i2i-220000000000002i−2i000000000000000000002i2i−2i−2i00000-220000000
χ3622-2-22-22-22-222-22-22-2-2-22−2i2i2i−2i-22−2i−2i2i2i-220000000000002i−2i00000000000000000000−2i−2i2i2i000002-20000000
χ3722-2-22-22-2-12-2-22-11-1111-12i−2i2i−2i-11−i−iii-112i−2i002-2000000−ii33−3−3−i3−i3i3i3−i3−i3i3i333−3−300000000−ii-110000000000
χ3822-2-22-22-2-12-2-22-11-1111-12i−2i2i−2i-11−i−iii-112i−2i002-2000000−ii−3−333i3i3−i3−i3i3i3−i3−i3−3−33300000000−ii-110000000000
χ3922-2-22-22-2-12-2-22-11-1111-12i−2i2i−2i-11−i−iii-11−2i2i00-22000000−ii33−3−3−i3−i3i3i3i3i3−i3−i3−3−33300000000i−i1-10000000000
χ4022-2-22-22-2-12-2-22-11-1111-12i−2i2i−2i-11−i−iii-11−2i2i00-22000000−ii−3−333i3i3−i3−i3−i3−i3i3i333−3−300000000i−i1-10000000000
χ4122-2-22-22-2-12-2-22-11-1111-1−2i2i−2i2i-11ii−i−i-112i−2i00-22000000i−i33−3−3i3i3−i3−i3−i3−i3i3i3−3−33300000000−ii1-10000000000
χ4222-2-22-22-2-12-2-22-11-1111-1−2i2i−2i2i-11ii−i−i-112i−2i00-22000000i−i−3−333−i3−i3i3i3i3i3−i3−i333−3−300000000−ii1-10000000000
χ4322-2-22-22-2-12-2-22-11-1111-1−2i2i−2i2i-11ii−i−i-11−2i2i002-2000000i−i33−3−3i3i3−i3−i3i3i3−i3−i333−3−300000000i−i-110000000000
χ4422-2-22-22-2-12-2-22-11-1111-1−2i2i−2i2i-11ii−i−i-11−2i2i002-2000000i−i−3−333−i3−i3i3i3−i3−i3i3i3−3−33300000000i−i-110000000000
χ452-22-222-2-22-22-22-222-22-2-20000-2-20000220000002i−2i00000000002i−2i2i−2i0000000000002i−2i2i−2i00000000002-200
χ462-22-222-2-22-22-22-222-22-2-20000-2-20000220000002i−2i00000000002i−2i2i−2i000000000000−2i2i−2i2i0000000000-2200
χ472-22-222-2-22-22-22-222-22-2-20000-2-2000022000000−2i2i0000000000−2i2i−2i2i0000000000002i−2i2i−2i0000000000-2200
χ482-22-222-2-22-22-22-222-22-2-20000-2-2000022000000−2i2i0000000000−2i2i−2i2i000000000000−2i2i−2i2i00000000002-200
χ492-2-222-2-22222-2-2-2-222-22-200002-20000-22002i−2i00000000002i−2i2i−2i00000000000000002-2-22000000002i−2i0000
χ502-2-222-2-22222-2-2-2-222-22-200002-20000-22002i−2i00000000002i−2i2i−2i0000000000000000-222-200000000−2i2i0000
χ512-2-222-2-22222-2-2-2-222-22-200002-20000-2200−2i2i0000000000−2i2i−2i2i00000000000000002-2-2200000000−2i2i0000
χ522-2-222-2-22222-2-2-2-222-22-200002-20000-2200−2i2i0000000000−2i2i−2i2i0000000000000000-222-2000000002i−2i0000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-422-2-2-2-2220000000000002200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422222222000000000000-2-200000000000000000000000000000000000000
χ554444-4-4-4-44000044-4-4-44-40000000000000000000000000000000000000000004-400000000000000000000
χ564444-4-4-4-44000044-4-4-44-4000000000000000000000000000000000000000000-4400000000000000000000
χ5744-4-44-44-4-2-444-4-22-2222-24i−4i−4i4i2-2−2i−2i2i2i2-20000000000002i−2i00000000000000000000000000000000000000
χ5844-4-44-44-4-2-444-4-22-2222-2−4i4i4i−4i2-22i2i−2i−2i2-2000000000000−2i2i00000000000000000000000000000000000000
χ5944-4-4-44-44400004-4-444-4-4000000000000000000000000000000000000000000004i−4i000000000000000000
χ6044-4-4-44-44400004-4-444-4-400000000000000000000000000000000000000000000−4i4i000000000000000000
χ614-44-444-4-444-44-4-444-44-4-40000440000-4-40000000000000000000000000000000000000000000000000000
χ624-44-444-4-4-24-44-42-2-22-2220000-2-200002200000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ634-44-444-4-4-24-44-42-2-22-2220000-2-2000022000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ644-44-444-4-4-2-44-442-2-22-2220000220000-2-20000004i−4i0000000000−2i2i−2i2i000000000000000000000000000000
χ654-44-444-4-4-2-44-442-2-22-2220000220000-2-2000000−4i4i00000000002i−2i2i−2i000000000000000000000000000000
χ664-44-4-4-44440000-44-44-4-44000000000000000000000022−22000000000022−2222−2200000000000000000000000000
χ674-44-4-4-44440000-44-44-4-440000000000000000000000−22220000000000−2222−222200000000000000000000000000
χ684-44-4-4-444-200002-22-222-200000023−2323−2300000000000022−220000000000−22−226−66−60000000000000000000000
χ694-44-4-4-444-200002-22-222-200000023−2323−23000000000000−222200000000002−22−2−66−660000000000000000000000
χ704-44-4-4-444-200002-22-222-2000000−2323−232300000000000022−220000000000−22−22−66−660000000000000000000000
χ714-44-4-4-444-200002-22-222-2000000−2323−2323000000000000−222200000000002−22−26−66−60000000000000000000000
χ724-4-444-4-444-4-444-4-444-44-40000-4400004-40000000000000000000000000000000000000000000000000000
χ734-4-444-4-44-244-4-422-2-22-220000-2200002-2004i−4i0000000000−2i2i−2i2i0000000000000000000000000000000000
χ744-4-444-4-44-244-4-422-2-22-220000-2200002-200−4i4i00000000002i−2i2i−2i0000000000000000000000000000000000
χ754-4-444-4-44-2-4-44422-2-22-2200002-20000-2200000000000000000023−23−2323000000000000000000000000000000
χ764-4-444-4-44-2-4-44422-2-22-2200002-20000-22000000000000000000−232323−23000000000000000000000000000000
χ774-4-44-444-440000-4-4-4-44440000000000000000000022−22000000000000000022−22−22220000000000000000000000
χ784-4-44-444-440000-4-4-4-444400000000000000000000−22220000000000000000−222222−220000000000000000000000
χ794-4-44-444-4-200002222-2-2-2000000−2i32i32i3−2i3000000000022−22000000000000−i6i6i6−i6−222−20000000000000000000000
χ804-4-44-444-4-200002222-2-2-2000000−2i32i32i3−2i30000000000−2222000000000000i6−i6−i6i62−2−220000000000000000000000
χ814-4-44-444-4-200002222-2-2-20000002i3−2i3−2i32i3000000000022−22000000000000i6−i6−i6i6−222−20000000000000000000000
χ824-4-44-444-4-200002222-2-2-20000002i3−2i3−2i32i30000000000−2222000000000000−i6i6i6−i62−2−220000000000000000000000
χ838888-8-8-8-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-88-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000

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