Finite Group Databasebeta

← Group #10944305

Character table — Group #10944305

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444444446666666688888888888812121212121212121212121216161616161616161616161648484848
order12222222344446666666224488888888121212128888888866121224242424242424242222444488882444661212121212122444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111-1-1-1-11-1-11
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-111-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111111-1-1-1-1-111-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-111111-1-11
χ911111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-1-11-11
χ1011111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-1111-11-1
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-111-1-111-1-11-11-1
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-111-1-111-1-111-11-11
χ1311111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11-11-111-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-11-11-1-11111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111111-11-111-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-11-11-1-11111-1-1-1-111
χ17222222222-2-2-2-2222222222-2-200000000-2-2-2-20000000022-2-20000000022-2-2-2-22200000000000000000000
χ18222222222-2-2-2-2222222222-2-200000000-2-2-2-20000000022-2-200000000-2-22222-2-200000000000000000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-200000000-2-222000000002222-2-2-2-200000000000000000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-200000000-2-22200000000-2-2-2-2222200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-100000000-1-1-1-1111111110000000000002-2-22-1-1-1-111110000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-100000000-1-1-1-111111111000000000000-222-21111-1-1-1-10000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1000000001111-1-1-1-1111100000000000022-2-2-1-111-1-1110000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1000000001111-1-1-1-11111000000000000-2-22211-1-111-1-10000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-10000000011111111-1-1-1-10000000000002-22-2-1-11111-1-10000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-10000000011111111-1-1-1-1000000000000-22-2211-1-1-1-1110000
χ2922-2-2-2-222222-2-22-2-222-2-22-22-22i2i−2i−2i2i2i−2i−2i22-2-2000000002-22-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ3022-2-2-2-222222-2-22-2-222-2-22-22-2−2i−2i2i2i−2i−2i2i2i22-2-2000000002-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ3122-2-2-2-222222-2-22-2-222-2-2-22-222i2i−2i−2i−2i−2i2i2i22-2-200000000-22-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ3222-2-2-2-222222-2-22-2-222-2-2-22-22−2i−2i2i2i2i2i−2i−2i22-2-200000000-22-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ3322-2-2-2-2222-2-2222-2-222-2-22-2-2200000000-2-2222222-2-2-2-22-2-22000000000000000022-2-20000000000000000
χ3422-2-2-2-2222-2-2222-2-222-2-22-2-2200000000-2-222-2-2-2-222222-2-220000000000000000-2-2220000000000000000
χ3522-2-2-2-2222-2-2222-2-222-2-2-222-200000000-2-2222222-2-2-2-2-222-20000000000000000-2-2220000000000000000
χ3622-2-2-2-2222-2-2222-2-222-2-2-222-200000000-2-222-2-2-2-22222-222-2000000000000000022-2-20000000000000000
χ3722-2-2-2-222-122-2-2-111-1-1112-22-22i2i−2i−2i2i2i−2i−2i-1-11100000000-11-11−i−iii−i−iii0000000000000000−i3i3−i3i33−33−30000
χ3822-2-2-2-222-122-2-2-111-1-1112-22-22i2i−2i−2i2i2i−2i−2i-1-11100000000-11-11−i−iii−i−iii0000000000000000i3−i3i3−i3−33−330000
χ3922-2-2-2-222-122-2-2-111-1-1112-22-2−2i−2i2i2i−2i−2i2i2i-1-11100000000-11-11ii−i−iii−i−i0000000000000000−i3i3−i3i3−33−330000
χ4022-2-2-2-222-122-2-2-111-1-1112-22-2−2i−2i2i2i−2i−2i2i2i-1-11100000000-11-11ii−i−iii−i−i0000000000000000i3−i3i3−i33−33−30000
χ4122-2-2-2-222-122-2-2-111-1-111-22-222i2i−2i−2i−2i−2i2i2i-1-111000000001-11-1−i−iiiii−i−i0000000000000000−i3i3i3−i33−3−330000
χ4222-2-2-2-222-122-2-2-111-1-111-22-222i2i−2i−2i−2i−2i2i2i-1-111000000001-11-1−i−iiiii−i−i0000000000000000i3−i3−i3i3−333−30000
χ4322-2-2-2-222-122-2-2-111-1-111-22-22−2i−2i2i2i2i2i−2i−2i-1-111000000001-11-1ii−i−i−i−iii0000000000000000−i3i3i3−i3−333−30000
χ4422-2-2-2-222-122-2-2-111-1-111-22-22−2i−2i2i2i2i2i−2i−2i-1-111000000001-11-1ii−i−i−i−iii0000000000000000i3−i3−i3i33−3−330000
χ452-22-22-22-222-22-2-22-22-22-2000000002i−2i2i−2i2-22-22i2i−2i−2i2i2i−2i−2i000000002i−2i2i−2i002-2002-200000000000000000000
χ462-22-22-22-222-22-2-22-22-22-2000000002i−2i2i−2i2-22-2−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i00-2200-2200000000000000000000
χ472-22-22-22-222-22-2-22-22-22-200000000−2i2i−2i2i2-22-22i2i−2i−2i2i2i−2i−2i00000000−2i2i−2i2i00-2200-2200000000000000000000
χ482-22-22-22-222-22-2-22-22-22-200000000−2i2i−2i2i2-22-2−2i−2i2i2i−2i−2i2i2i00000000−2i2i−2i2i002-2002-200000000000000000000
χ492-22-22-22-22-22-22-22-22-22-200002-22-20000-22-220000000000002-22-20000002-200-222-22-20000000000000000
χ502-22-22-22-22-22-22-22-22-22-200002-22-20000-22-220000000000002-22-2000000-22002-2-22-220000000000000000
χ512-22-22-22-22-22-22-22-22-22-20000-22-220000-22-22000000000000-22-220000002-200-22-22-220000000000000000
χ522-22-22-22-22-22-22-22-22-22-20000-22-220000-22-22000000000000-22-22000000-22002-22-22-20000000000000000
χ532-2-22-222-222-2-22-2-222-2-22000000002-2-222-2-2200000000000000002-2-222-2002-2002-2-220000000000000000
χ542-2-22-222-222-2-22-2-222-2-22000000002-2-222-2-2200000000000000002-2-22-2200-2200-222-20000000000000000
χ552-2-22-222-222-2-22-2-222-2-2200000000-222-22-2-220000000000000000-222-22-2002-200-222-20000000000000000
χ562-2-22-222-222-2-22-2-222-2-2200000000-222-22-2-220000000000000000-222-2-2200-22002-2-220000000000000000
χ572-2-22-222-22-222-2-2-222-2-2200002i−2i−2i2i0000-222-22i2i−2i−2i−2i−2i2i2i00002i−2i−2i2i0000-22002-20000000000000000000000
χ582-2-22-222-22-222-2-2-222-2-2200002i−2i−2i2i0000-222-2−2i−2i2i2i2i2i−2i−2i00002i−2i−2i2i00002-200-220000000000000000000000
χ592-2-22-222-22-222-2-2-222-2-220000−2i2i2i−2i0000-222-22i2i−2i−2i−2i−2i2i2i0000−2i2i2i−2i00002-200-220000000000000000000000
χ602-2-22-222-22-222-2-2-222-2-220000−2i2i2i−2i0000-222-2−2i−2i2i2i2i2i−2i−2i0000−2i2i2i−2i0000-22002-20000000000000000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-244-4-400000000222200000000-2-222000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000000022220000000022-2-2000000000000000000000000000000000000
χ634444-4-4-4-4400004-4-4-4-4440000000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ644444-4-4-4-4400004-4-4-4-44400000000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ6544-4-444-4-440000444-4-4-4-40000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ6644-4-444-4-440000444-4-4-4-400000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ6744-4-4-4-444-2-4-444-222-2-2224-4-440000000022-2-200000000-222-2000000000000000000000000000000000000
χ6844-4-4-4-444-2-4-444-222-2-222-444-40000000022-2-2000000002-2-22000000000000000000000000000000000000
χ694-44-44-44-4-24-44-42-22-22-22000000004i−4i4i−4i-22-220000000000000000−2i2i−2i2i0000000000000000000000000000
χ704-44-44-44-4-24-44-42-22-22-2200000000−4i4i−4i4i-22-2200000000000000002i−2i2i−2i0000000000000000000000000000
χ714-44-44-44-4-2-44-442-22-22-2200004-44-400002-22-2000000000000-22-2200000000000000000000000000000000
χ724-44-44-44-4-2-44-442-22-22-220000-44-4400002-22-20000000000002-22-200000000000000000000000000000000
χ734-44-4-44-4440000-4-44-444-4000000000000000022−22−222222−22−22220000000000000000000000000000000000000000
χ744-44-4-44-4440000-4-44-444-40000000000000000−222222−22−222222−220000000000000000000000000000000000000000
χ754-4-444-4-4440000-44-4-44-44000000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ764-4-444-4-4440000-44-4-44-440000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ774-4-44-444-4-24-4-4422-2-222-2000000004-4-44-222-20000000000000000-222-20000000000000000000000000000
χ784-4-44-444-4-24-4-4422-2-222-200000000-444-4-222-200000000000000002-2-220000000000000000000000000000
χ794-4-44-444-4-2-444-422-2-222-200004i−4i−4i4i00002-2-22000000000000−2i2i2i−2i00000000000000000000000000000000
χ804-4-44-444-4-2-444-422-2-222-20000−4i4i4i−4i00002-2-220000000000002i−2i−2i2i00000000000000000000000000000000
χ818888-8-8-8-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000
χ8288-8-888-8-8-40000-4-4-444440000000000000000000000000000000000000000000000000000000000000000
χ838-88-8-88-88-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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