Finite Group Databasebeta

← Group #10945047

Character table — Group #10945047

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888812121212121212121212121212121212161616161616242424244848
order12222222344446666666222244444444121212121212121266668888121212121212242424242424242422222244444444444412121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11-111-1-111-1-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111111-111-1-1-1-111-11
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-11-1-111-1-111-11
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-11-1-11111-1-11-1
χ911111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-11-1-111-1-1111-1
χ1011111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-11-1-11111-1-1-11
χ1111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-11-111-1-111-1-1-11
χ1211111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111111-111-1-1-1-1111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111
χ17222222222-2-2-2-222222220000000022-2-2-2-22222-2-200000000-2-2000000000000000022-2-2-2-2220000000000000000
χ18222222222-2-2-2-222222220000000022-2-2-2-22222-2-200000000-2-20000000000000000-2-22222-2-20000000000000000
χ19222222222-2-2-2-2222222200000000-2-222-2-2-2-2-2-2-2-2000000002200000000000000002222-2-2-2-20000000000000000
χ20222222222-2-2-2-2222222200000000-2-222-2-2-2-2-2-2-2-200000000220000000000000000-2-2-2-222220000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1000000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000000000000000-2-21111000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-11111-1-1-1-1-1-122-2-2111111-1-1-1-1111100000000000000002-2-1-111000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-11111-1-1-1-1-1-1-2-2221111111111-1-1-1-10000000000000000-2211-1-1000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-11111-1-1111122-2-211-1-1-1-1-1-1-1-111110000000000000000-2211-1-1000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-11111-1-11111-2-22211-1-1-1-11111-1-1-1-100000000000000002-2-1-111000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-111112222-1-11111-1-1-1-1-1-1-1-10000000000000000-2-21111000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1111111111111000000000000000022-1-1-1-1000000
χ2922-22-2-22-222-22-22-2-22-22-2000000002i−2i2i−2i2-22i2i−2i−2i2-2000000002i−2i00000000000022-2-2000000002i2i−2i−2i000000000000
χ3022-22-2-22-222-22-22-2-22-22-2000000002i−2i2i−2i2-22i2i−2i−2i2-2000000002i−2i000000000000-2-22200000000−2i−2i2i2i000000000000
χ3122-22-2-22-222-22-22-2-22-22-200000000−2i2i−2i2i2-2−2i−2i2i2i2-200000000−2i2i00000000000022-2-200000000−2i−2i2i2i000000000000
χ3222-22-2-22-222-22-22-2-22-22-200000000−2i2i−2i2i2-2−2i−2i2i2i2-200000000−2i2i000000000000-2-222000000002i2i−2i−2i000000000000
χ3322-22-2-22-22-22-222-2-22-22-222-2-22i2i−2i−2i2i−2i−2i2i-222i2i−2i−2i-2222-2-20000−2i2i2i2i−2i−2i000000000000000000000000000000000000
χ3422-22-2-22-22-22-222-2-22-22-222-2-2−2i−2i2i2i−2i2i2i−2i-22−2i−2i2i2i-2222-2-200002i−2i−2i−2i2i2i000000000000000000000000000000000000
χ3522-22-2-22-22-22-222-2-22-22-2-2-2222i2i−2i−2i−2i2i2i−2i-22−2i−2i2i2i-22-2-22200002i−2i2i2i−2i−2i000000000000000000000000000000000000
χ3622-22-2-22-22-22-222-2-22-22-2-2-222−2i−2i2i2i2i−2i−2i2i-222i2i−2i−2i-22-2-2220000−2i2i−2i−2i2i2i000000000000000000000000000000000000
χ3722-22-2-22-2-1-22-22-111-11-1122-2-22i2i−2i−2i2i−2i−2i2i1-1−i−iii1-1-1-1110000i−i−i−iii−i3−i3i3i333−3−3000000000000000000−i3i33−3000000
χ3822-22-2-22-2-1-22-22-111-11-1122-2-22i2i−2i−2i2i−2i−2i2i1-1−i−iii1-1-1-1110000i−i−i−iiii3i3−i3−i3−3−333000000000000000000i3−i3−33000000
χ3922-22-2-22-2-1-22-22-111-11-1122-2-2−2i−2i2i2i−2i2i2i−2i1-1ii−i−i1-1-1-1110000−iiii−i−i−i3−i3i3i3−3−333000000000000000000−i3i3−33000000
χ4022-22-2-22-2-1-22-22-111-11-1122-2-2−2i−2i2i2i−2i2i2i−2i1-1ii−i−i1-1-1-1110000−iiii−i−ii3i3−i3−i333−3−3000000000000000000i3−i33−3000000
χ4122-22-2-22-2-1-22-22-111-11-11-2-2222i2i−2i−2i−2i2i2i−2i1-1ii−i−i1-111-1-10000−ii−i−iii−i3−i3i3i3−3−333000000000000000000i3−i33−3000000
χ4222-22-2-22-2-1-22-22-111-11-11-2-2222i2i−2i−2i−2i2i2i−2i1-1ii−i−i1-111-1-10000−ii−i−iiii3i3−i3−i333−3−3000000000000000000−i3i3−33000000
χ4322-22-2-22-2-1-22-22-111-11-11-2-222−2i−2i2i2i2i−2i−2i2i1-1−i−iii1-111-1-10000i−iii−i−i−i3−i3i3i333−3−3000000000000000000i3−i3−33000000
χ4422-22-2-22-2-1-22-22-111-11-11-2-222−2i−2i2i2i2i−2i−2i2i1-1−i−iii1-111-1-10000i−iii−i−ii3i3−i3−i3−3−333000000000000000000−i3i33−3000000
χ452-22-22-22-2222-2-2-2222-2-2-200002i−2i2i−2i0000-2-200002200000000002i−2i2i−2i000000002-22-2002i−2i002i−2i0000000000000000
χ462-22-22-22-2222-2-2-2222-2-2-200002i−2i2i−2i0000-2-200002200000000002i−2i2i−2i00000000-22-2200−2i2i00−2i2i0000000000000000
χ472-22-22-22-2222-2-2-2222-2-2-20000−2i2i−2i2i0000-2-20000220000000000−2i2i−2i2i000000002-22-200−2i2i00−2i2i0000000000000000
χ482-22-22-22-2222-2-2-2222-2-2-20000−2i2i−2i2i0000-2-20000220000000000−2i2i−2i2i00000000-22-22002i−2i002i−2i0000000000000000
χ492-22-22-22-22-2-222-2222-2-2-22-22-200000000220000-2-22-22-20000000000000000000000002i−2i00−2i2i2i−2i2i−2i000000000000
χ502-22-22-22-22-2-222-2222-2-2-22-22-200000000220000-2-22-22-2000000000000000000000000−2i2i002i−2i−2i2i−2i2i000000000000
χ512-22-22-22-22-2-222-2222-2-2-2-22-2200000000220000-2-2-22-220000000000000000000000002i−2i00−2i2i−2i2i−2i2i000000000000
χ522-22-22-22-22-2-222-2222-2-2-2-22-2200000000220000-2-2-22-22000000000000000000000000−2i2i002i−2i2i−2i2i−2i000000000000
χ532-2-2-2-222222-2-22-2-2-222-222-2-2200000000-2200002-22-2-220000000000000000002-2-222-2002-2000000000000000000
χ542-2-2-2-222222-2-22-2-2-222-222-2-2200000000-2200002-22-2-22000000000000000000-222-2-2200-22000000000000000000
χ552-2-2-2-222222-2-22-2-2-222-22-222-200000000-2200002-2-222-20000000000000000002-2-22-2200-22000000000000000000
χ562-2-2-2-222222-2-22-2-2-222-22-222-200000000-2200002-2-222-2000000000000000000-222-22-2002-2000000000000000000
χ572-2-2-2-22222-222-2-2-2-222-2200002-2-2200002-20000-2200000000002-2-220000000000002-200-2200-222-2000000000000
χ582-2-2-2-22222-222-2-2-2-222-2200002-2-2200002-20000-2200000000002-2-22000000000000-22002-2002-2-22000000000000
χ592-2-2-2-22222-222-2-2-2-222-220000-222-200002-20000-220000000000-222-20000000000002-200-22002-2-22000000000000
χ602-2-2-2-22222-222-2-2-2-222-220000-222-200002-20000-220000000000-222-2000000000000-22002-200-222-2000000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000000044-4-422-2-2-2-22200000000220000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-200000000-4-4442222222200000000-2-20000000000000000000000000000000000000000
χ63444-4-44-4-44000044-4-4-4-440000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ64444-4-44-4-44000044-4-4-4-4400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ6544-44-4-44-4-24-44-4-222-22-22000000004i−4i4i−4i-22−2i−2i2i2i-2200000000−2i2i0000000000000000000000000000000000000000
χ6644-44-4-44-4-24-44-4-222-22-2200000000−4i4i−4i4i-222i2i−2i−2i-22000000002i−2i0000000000000000000000000000000000000000
χ6744-4-44-4-44400004-44-44-4-4000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ6844-4-44-4-44400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ694-444-4-4-4440000-44-4-444-400000000000000000000000000−2i22i20000000000−2i22i2−2i22i20000000000000000000000000000
χ704-444-4-4-4440000-44-4-444-4000000000000000000000000002i2−2i200000000002i2−2i22i2−2i20000000000000000000000000000
χ714-444-4-4-44-200002-222-2-220000000000000023−2323−2300000000−2i22i2000000i6−i6i6−i6i2−i2i2−i20000000000000000000000000000
χ724-444-4-4-44-200002-222-2-220000000000000023−2323−23000000002i2−2i2000000−i6i6−i6i6−i2i2−i2i20000000000000000000000000000
χ734-444-4-4-44-200002-222-2-2200000000000000−2323−232300000000−2i22i2000000−i6i6−i6i6i2−i2i2−i20000000000000000000000000000
χ744-444-4-4-44-200002-222-2-2200000000000000−2323−2323000000002i2−2i2000000i6−i6i6−i6−i2i2−i2i20000000000000000000000000000
χ754-44-44-44-4-244-4-42-2-2-222200004i−4i4i−4i0000220000-2-20000000000−2i2i−2i2i000000000000000000000000000000000000
χ764-44-44-44-4-244-4-42-2-2-22220000−4i4i−4i4i0000220000-2-200000000002i−2i2i−2i000000000000000000000000000000000000
χ774-44-44-44-4-2-4-4442-2-2-22224-44-400000000-2-2000022-22-220000000000000000000000000000000000000000000000
χ784-44-44-44-4-2-4-4442-2-2-2222-44-4400000000-2-20000222-22-20000000000000000000000000000000000000000000000
χ794-4-4444-4-440000-4-44-4-44400000000000000000000000022−220000000022−22−222200000000000000000000000000000000
χ804-4-4444-4-440000-4-44-4-444000000000000000000000000−222200000000−222222−2200000000000000000000000000000000
χ814-4-4444-4-4-2000022-222-2-200000000000000−2i32i32i3−2i300000022−2200000000−222−2−i6i6i6−i60000000000000000000000000000
χ824-4-4444-4-4-2000022-222-2-200000000000000−2i32i32i3−2i3000000−2222000000002−2−22i6−i6−i6i60000000000000000000000000000
χ834-4-4444-4-4-2000022-222-2-2000000000000002i3−2i3−2i32i300000022−2200000000−222−2i6−i6−i6i60000000000000000000000000000
χ844-4-4444-4-4-2000022-222-2-2000000000000002i3−2i3−2i32i3000000−2222000000002−2−22−i6i6i6−i60000000000000000000000000000
χ854-4-4-4-4444-24-4-44222-2-22-24-4-44000000002-20000-22-222-20000000000000000000000000000000000000000000000
χ864-4-4-4-4444-24-4-44222-2-22-2-444-4000000002-20000-222-2-220000000000000000000000000000000000000000000000
χ874-4-4-4-4444-2-444-4222-2-22-200004-4-440000-2200002-20000000000-222-2000000000000000000000000000000000000
χ884-4-4-4-4444-2-444-4222-2-22-20000-444-40000-2200002-200000000002-2-22000000000000000000000000000000000000
χ89888-8-88-8-8-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-88-8-88-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000

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