Finite Group Databasebeta

← Group #10945058

Character table — Group #10945058

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888812121212121212121212121212121212161616161616242424244848
order122222223444466666664444444444441212121212121212888812121212121212121212242424242424242422444444444444444412121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-111-1-1-1-11-111-1-111-1-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111111-111-1-1-1-111-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-11-1-111-1-111-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-11-1-11111-1-11-1
χ911111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-11-1-11111-1-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1-111-1-1111-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111-111-1-1-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11-111-1-111-1-1-11
χ17222222222-2-2-2-22222222000022-2-20000-2-2-2-2-2-2-2-2000000000000220000000022-2-2000022-2-20000000000000000
χ18222222222-2-2-2-22222222000022-2-20000-2-2-2-2-2-2-2-20000000000002200000000-2-2220000-2-2220000000000000000
χ19222222222-2-2-2-222222220000-2-22200002222-2-2-2-2000000000000-2-20000000022220000-2-2-2-20000000000000000
χ20222222222-2-2-2-222222220000-2-22200002222-2-2-2-2000000000000-2-200000000-2-2-2-2000022220000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1000000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-21111000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-21111-1-1-1-122-2-21111-1-1-1-111-1-1-1-1111100000000000000002-2-1-111000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-21111-1-1-1-1-2-2221111-1-1-1-1111111-1-1-1-10000000000000000-2211-1-1000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1222211111111-1-1-1-1-1-1-1-1-1-10000000000000000-2-21111000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-211111111-1-111111111000000000000000022-1-1-1-1000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-1-1-122-2-2-1-1-1-1111111-1-1-1-111110000000000000000-2211-1-1000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-1-1-1-2-222-1-1-1-11111111111-1-1-1-100000000000000002-2-1-111000000
χ2922-22-2-2-2222-22-22-2-2-222-200002i−2i2i−2i00002i2i−2i−2i2-22-20000000000002i−2i0000000000002i2i−2i−2i000022-2-2000000000000
χ3022-22-2-2-2222-22-22-2-2-222-200002i−2i2i−2i00002i2i−2i−2i2-22-20000000000002i−2i000000000000−2i−2i2i2i0000-2-222000000000000
χ3122-22-2-2-2222-22-22-2-2-222-20000−2i2i−2i2i0000−2i−2i2i2i2-22-2000000000000−2i2i0000000000002i2i−2i−2i0000-2-222000000000000
χ3222-22-2-2-2222-22-22-2-2-222-20000−2i2i−2i2i0000−2i−2i2i2i2-22-2000000000000−2i2i000000000000−2i−2i2i2i000022-2-2000000000000
χ3322-22-2-2-222-22-222-2-2-222-22i2i−2i−2i2i−2i−2i2i22-2-2−2i−2i2i2i-22-22000022-2-22i2i−2i−2i2i−2i000000000000000000000000000000000000
χ3422-22-2-2-222-22-222-2-2-222-22i2i−2i−2i−2i2i2i−2i-2-2222i2i−2i−2i-22-220000-2-2222i2i−2i−2i−2i2i000000000000000000000000000000000000
χ3522-22-2-2-222-22-222-2-2-222-2−2i−2i2i2i2i−2i−2i2i-2-222−2i−2i2i2i-22-220000-2-222−2i−2i2i2i2i−2i000000000000000000000000000000000000
χ3622-22-2-2-222-22-222-2-2-222-2−2i−2i2i2i−2i2i2i−2i22-2-22i2i−2i−2i-22-22000022-2-2−2i−2i2i2i−2i2i000000000000000000000000000000000000
χ3722-22-2-2-22-1-22-22-1111-1-112i2i−2i−2i2i−2i−2i2i22-2-2ii−i−i1-11-10000-1-111−i−iii−ii33−3−3−i3−i3i3i3000000000000000000−i3i33−3000000
χ3822-22-2-2-22-1-22-22-1111-1-112i2i−2i−2i2i−2i−2i2i22-2-2ii−i−i1-11-10000-1-111−i−iii−ii−3−333i3i3−i3−i3000000000000000000i3−i3−33000000
χ3922-22-2-2-22-1-22-22-1111-1-112i2i−2i−2i−2i2i2i−2i-2-222−i−iii1-11-1000011-1-1−i−iiii−i33−3−3i3i3−i3−i3000000000000000000−i3i3−33000000
χ4022-22-2-2-22-1-22-22-1111-1-112i2i−2i−2i−2i2i2i−2i-2-222−i−iii1-11-1000011-1-1−i−iiii−i−3−333−i3−i3i3i3000000000000000000i3−i33−3000000
χ4122-22-2-2-22-1-22-22-1111-1-11−2i−2i2i2i2i−2i−2i2i-2-222ii−i−i1-11-1000011-1-1ii−i−i−ii33−3−3−i3−i3i3i3000000000000000000i3−i3−33000000
χ4222-22-2-2-22-1-22-22-1111-1-11−2i−2i2i2i2i−2i−2i2i-2-222ii−i−i1-11-1000011-1-1ii−i−i−ii−3−333i3i3−i3−i3000000000000000000−i3i33−3000000
χ4322-22-2-2-22-1-22-22-1111-1-11−2i−2i2i2i−2i2i2i−2i22-2-2−i−iii1-11-10000-1-111ii−i−ii−i33−3−3i3i3−i3−i3000000000000000000i3−i33−3000000
χ4422-22-2-2-22-1-22-22-1111-1-11−2i−2i2i2i−2i2i2i−2i22-2-2−i−iii1-11-10000-1-111ii−i−ii−i−3−333−i3−i3i3i3000000000000000000−i3i3−33000000
χ452-22-22-2-22222-2-2-222-2-22-22i−2i2i−2i000000000000-2-222000000002i−2i2i−2i0000000000002i−2i00002i−2i002-22-2000000000000
χ462-22-22-2-22222-2-2-222-2-22-22i−2i2i−2i000000000000-2-222000000002i−2i2i−2i000000000000−2i2i0000−2i2i00-22-22000000000000
χ472-22-22-2-22222-2-2-222-2-22-2−2i2i−2i2i000000000000-2-22200000000−2i2i−2i2i0000000000002i−2i00002i−2i00-22-22000000000000
χ482-22-22-2-22222-2-2-222-2-22-2−2i2i−2i2i000000000000-2-22200000000−2i2i−2i2i000000000000−2i2i0000−2i2i002-22-2000000000000
χ492-22-22-2-222-2-222-222-2-22-2000000002-22-2000022-2-200002-22-200000000000000002i−2i2i−2i2i−2i−2i2i000000000000000000
χ502-22-22-2-222-2-222-222-2-22-2000000002-22-2000022-2-200002-22-20000000000000000−2i2i−2i2i−2i2i2i−2i000000000000000000
χ512-22-22-2-222-2-222-222-2-22-200000000-22-22000022-2-20000-22-2200000000000000002i−2i−2i2i−2i2i−2i2i000000000000000000
χ522-22-22-2-222-2-222-222-2-22-200000000-22-22000022-2-20000-22-220000000000000000−2i2i2i−2i2i−2i2i−2i000000000000000000
χ532-2-2-2-222222-2-22-2-2-22-222000000002-2-220000-222-200002-2-22000000000000002-2000000002-22-2-22000000000000
χ542-2-2-2-222222-2-22-2-2-22-222000000002-2-220000-222-200002-2-2200000000000000-2200000000-22-222-2000000000000
χ552-2-2-2-222222-2-22-2-2-22-22200000000-222-20000-222-20000-222-2000000000000002-2000000002-2-222-2000000000000
χ562-2-2-2-222222-2-22-2-2-22-22200000000-222-20000-222-20000-222-200000000000000-2200000000-222-2-22000000000000
χ572-2-2-2-22222-222-2-2-2-22-2222-2-220000000000002-2-22000000002-2-2200000000002-200-222-200-220000000000000000
χ582-2-2-2-22222-222-2-2-2-22-2222-2-220000000000002-2-22000000002-2-220000000000-22002-2-22002-20000000000000000
χ592-2-2-2-22222-222-2-2-2-22-222-222-20000000000002-2-2200000000-222-200000000002-2002-2-2200-220000000000000000
χ602-2-2-2-22222-222-2-2-2-22-222-222-20000000000002-2-2200000000-222-20000000000-2200-222-2002-20000000000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-4000022222222000000000000-2-2000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4440000-2-2-2-2222200000000000022000000000000000000000000000000000000
χ63444-4-44-4-44000044-4-4-4-44000000000000000000000022−220000000000000022−2222−220000000000000000000000000000
χ64444-4-44-4-44000044-4-4-4-440000000000000000000000−222200000000000000−2222−22220000000000000000000000000000
χ65444-4-44-4-4-20000-2-22222-200000000000023−2323−2300000022−2200000000006−66−6−22−220000000000000000000000000000
χ66444-4-44-4-4-20000-2-22222-200000000000023−2323−23000000−22220000000000−66−662−22−20000000000000000000000000000
χ67444-4-44-4-4-20000-2-22222-2000000000000−2323−232300000022−220000000000−66−66−22−220000000000000000000000000000
χ68444-4-44-4-4-20000-2-22222-2000000000000−2323−2323000000−222200000000006−66−62−22−20000000000000000000000000000
χ6944-44-4-4-44-24-44-4-2222-2-2200004i−4i4i−4i0000−2i−2i2i2i-22-22000000000000−2i2i000000000000000000000000000000000000
χ7044-44-4-4-44-24-44-4-2222-2-220000−4i4i−4i4i00002i2i−2i−2i-22-220000000000002i−2i000000000000000000000000000000000000
χ7144-4-44-44-4400004-444-4-4-40000000000000000000022−2200000000000022−22−222200000000000000000000000000000000
χ7244-4-44-44-4400004-444-4-4-400000000000000000000−2222000000000000−222222−2200000000000000000000000000000000
χ7344-4-44-44-4-20000-22-2-2222000000000000−2i32i32i3−2i3000022−22000000000000−222−2i6−i6−i6i60000000000000000000000000000
χ7444-4-44-44-4-20000-22-2-2222000000000000−2i32i32i3−2i30000−22220000000000002−2−22−i6i6i6−i60000000000000000000000000000
χ7544-4-44-44-4-20000-22-2-22220000000000002i3−2i3−2i32i3000022−22000000000000−222−2−i6i6i6−i60000000000000000000000000000
χ7644-4-44-44-4-20000-22-2-22220000000000002i3−2i3−2i32i30000−22220000000000002−2−22i6−i6−i6i60000000000000000000000000000
χ774-444-4-44-440000-44-444-4-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ784-444-4-44-440000-44-444-4-40000000000000000000000000000000000000000000000000000000000000000−22220000
χ794-44-44-4-44-244-4-42-2-222-224i−4i4i−4i00000000000022-2-200000000−2i2i−2i2i00000000000000000000000000000000000000
χ804-44-44-4-44-244-4-42-2-222-22−4i4i−4i4i00000000000022-2-2000000002i−2i2i−2i00000000000000000000000000000000000000
χ814-44-44-4-44-2-4-4442-2-222-22000000004-44-40000-2-2220000-22-22000000000000000000000000000000000000000000
χ824-44-44-4-44-2-4-4442-2-222-2200000000-44-440000-2-22200002-22-2000000000000000000000000000000000000000000
χ834-4-4444-4-440000-4-44-44-44000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ844-4-4444-4-440000-4-44-44-440000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ854-4-4-4-4444-24-4-44222-22-2-2000000004-4-4400002-2-220000-222-2000000000000000000000000000000000000000000
χ864-4-4-4-4444-24-4-44222-22-2-200000000-444-400002-2-2200002-2-22000000000000000000000000000000000000000000
χ874-4-4-4-4444-2-444-4222-22-2-24-4-44000000000000-222-200000000-222-200000000000000000000000000000000000000
χ884-4-4-4-4444-2-444-4222-22-2-2-444-4000000000000-222-2000000002-2-2200000000000000000000000000000000000000
χ898-888-8-88-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8888-8-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000

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