Finite Group Databasebeta

← Group #10858325

Character table — Group #10858325

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444422224444441212121212121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1111-1-11-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-111-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-111-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111111-1-1111-1-1-1-1
χ91111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1111-1-1-1-111111-1-1-1-1-1-1-111
χ101111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1111-1-1-1-111-1-1-11111111-1-1
χ111111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-11111-1-111-1-1-1-1-1111-1-1
χ121111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1-1-11111-1-1-1-111111-1-1-111
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1111111-1-11-11111-1-1-1-1-1-11-1-111-111-1-1
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11111-1-1-1-111-111-1-11-1-111
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-111-11-1-1-1-11111-1-1-1-1-1111-1-111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-11-1-1-1-1111111111-1-1-111-1-1
χ17222222222-22222-2-2-22222222-2-200000000-2-22222-2-2-2-2-2-20000000000000000000000002222000000000000-20000-20000
χ18222222222-22222-2-2-22222222-2-200000000-2-22222-2-2-2-2-2-2000000000000000000000000-2-2-2-20000000000002000020000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-200000000000000000000000022-2-2000000000000-2000020000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-2000000000000000000000000-2-22200000000000020000-20000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-111-1-111000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-2000000002211-1-111-1-1000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-200000000-22-1-11111-1-1000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-222000000002-211-1-1-1-111000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-122-2-2000000002-2-1-1-1-11111000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-2-22200000000-221111-1-1-1-1000000000000
χ292222-2-2-2-22200002-2-2222-2-2-2-20022-2-200002-2000000002-22222-2-2-2-200000000000022-2-2000000000000002-20000000000
χ302222-2-2-2-22200002-2-2222-2-2-2-20022-2-200002-2000000002-22222-2-2-2-2000000000000-2-22200000000000000-220000000000
χ312222-2-2-2-22200002-2-2222-2-2-2-200-2-22200002-2000000002-2-2-2-2-2222200000000000022-2-200000000000000-220000000000
χ322222-2-2-2-22200002-2-2222-2-2-2-200-2-22200002-2000000002-2-2-2-2-22222000000000000-2-222000000000000002-20000000000
χ3322-2-22-22-2202i2i−2i−2i0002-2-22-22-2002−22−2−i2−i2i2i2002i2i−2i−2i00000022−2−222−2−2−i2−i2−i2−i2i2i2i2i2000000002i−2i2-20000000000000000002−2−i2i2
χ3422-2-22-22-2202i2i−2i−2i0002-2-22-22-2002−22−2−i2−i2i2i2002i2i−2i−2i00000022−2−222−2−2−i2−i2−i2−i2i2i2i2i200000000−2i2i-22000000000000000000−22i2−i2
χ3522-2-22-22-2202i2i−2i−2i0002-2-22-22-200−22−22i2i2−i2−i2002i2i−2i−2i000000−2−222−2−222i2i2i2i2−i2−i2−i2−i2000000002i−2i2-2000000000000000000−22i2−i2
χ3622-2-22-22-2202i2i−2i−2i0002-2-22-22-200−22−22i2i2−i2−i2002i2i−2i−2i000000−2−222−2−222i2i2i2i2−i2−i2−i2−i200000000−2i2i-220000000000000000002−2−i2i2
χ3722-2-22-22-220−2i−2i2i2i0002-2-22-22-2002−22−2i2i2−i2−i200−2i−2i2i2i00000022−2−222−2−2i2i2i2i2−i2−i2−i2−i2000000002i−2i-22000000000000000000−22−i2i2
χ3822-2-22-22-220−2i−2i2i2i0002-2-22-22-2002−22−2i2i2−i2−i200−2i−2i2i2i00000022−2−222−2−2i2i2i2i2−i2−i2−i2−i200000000−2i2i2-20000000000000000002−2i2−i2
χ3922-2-22-22-220−2i−2i2i2i0002-2-22-22-200−22−22−i2−i2i2i200−2i−2i2i2i000000−2−222−2−222−i2−i2−i2−i2i2i2i2i2000000002i−2i-220000000000000000002−2i2−i2
χ4022-2-22-22-220−2i−2i2i2i0002-2-22-22-200−22−22−i2−i2i2i200−2i−2i2i2i000000−2−222−2−222−i2−i2−i2−i2i2i2i2i200000000−2i2i2-2000000000000000000−22−i2i2
χ412-2-2222-2-2222i−2i2i−2i-2-22-2-2222-2-22i−2i000000002-22i−2i2i−2i2i2i−2i−2i-2200000000000000002-22i−2i00000000002-2002i−2i00000000000000
χ422-2-2222-2-2222i−2i2i−2i-2-22-2-2222-2-22i−2i000000002-22i−2i2i−2i2i2i−2i−2i-220000000000000000-22−2i2i0000000000-2200−2i2i00000000000000
χ432-2-2222-2-222−2i2i−2i2i-2-22-2-2222-2-2−2i2i000000002-2−2i2i−2i2i−2i−2i2i2i-2200000000000000002-2−2i2i00000000002-200−2i2i00000000000000
χ442-2-2222-2-222−2i2i−2i2i-2-22-2-2222-2-2−2i2i000000002-2−2i2i−2i2i−2i−2i2i2i-220000000000000000-222i−2i0000000000-22002i−2i00000000000000
χ452-2-2222-2-22-22i−2i2i−2i22-2-2-2222-2-2−2i2i00000000-222i−2i2i−2i−2i−2i2i2i2-2000000000000000000002-22-2000000000000000002i−2i0000000
χ462-2-2222-2-22-22i−2i2i−2i22-2-2-2222-2-2−2i2i00000000-222i−2i2i−2i−2i−2i2i2i2-200000000000000000000-22-2200000000000000000−2i2i0000000
χ472-2-2222-2-22-2−2i2i−2i2i22-2-2-2222-2-22i−2i00000000-22−2i2i−2i2i2i2i−2i−2i2-2000000000000000000002-22-200000000000000000−2i2i0000000
χ482-2-2222-2-22-2−2i2i−2i2i22-2-2-2222-2-22i−2i00000000-22−2i2i−2i2i2i2i−2i−2i2-200000000000000000000-22-22000000000000000002i−2i0000000
χ492-2-2222-2-2-122i−2i2i−2i-2-2211-1-1-1112i−2i00000000-11−ii−ii−i−iii1-13−33−33−33−3−i3−i3i3i3−i3−i3i3i32-22i−2i0000000000-11−i3i3−ii3−3000000000000
χ502-2-2222-2-2-122i−2i2i−2i-2-2211-1-1-1112i−2i00000000-11−ii−ii−i−iii1-13−33−33−33−3−i3−i3i3i3−i3−i3i3i3-22−2i2i00000000001-1i3−i3i−i−33000000000000
χ512-2-2222-2-2-122i−2i2i−2i-2-2211-1-1-1112i−2i00000000-11−ii−ii−i−iii1-1−33−33−33−33i3i3−i3−i3i3i3−i3−i32-22i−2i0000000000-11i3−i3−ii−33000000000000
χ522-2-2222-2-2-122i−2i2i−2i-2-2211-1-1-1112i−2i00000000-11−ii−ii−i−iii1-1−33−33−33−33i3i3−i3−i3i3i3−i3−i3-22−2i2i00000000001-1−i3i3i−i3−3000000000000
χ532-2-2222-2-2-12−2i2i−2i2i-2-2211-1-1-111−2i2i00000000-11i−ii−iii−i−i1-13−33−33−33−3i3i3−i3−i3i3i3−i3−i32-2−2i2i0000000000-11i3−i3i−i3−3000000000000
χ542-2-2222-2-2-12−2i2i−2i2i-2-2211-1-1-111−2i2i00000000-11i−ii−iii−i−i1-13−33−33−33−3i3i3−i3−i3i3i3−i3−i3-222i−2i00000000001-1−i3i3−ii−33000000000000
χ552-2-2222-2-2-12−2i2i−2i2i-2-2211-1-1-111−2i2i00000000-11i−ii−iii−i−i1-1−33−33−33−33−i3−i3i3i3−i3−i3i3i32-2−2i2i0000000000-11−i3i3i−i−33000000000000
χ562-2-2222-2-2-12−2i2i−2i2i-2-2211-1-1-111−2i2i00000000-11i−ii−iii−i−i1-1−33−33−33−33−i3−i3i3i3−i3−i3i3i3-222i−2i00000000001-1i3−i3−ii3−3000000000000
χ572-2-22-2-2222-200002-22-2-22-2-2220000002-22-2-2-20000000022000000002-22-22-22-200002-2-2200000000000000000002-200000
χ582-2-22-2-2222-200002-22-2-22-2-2220000002-22-2-2-20000000022000000002-22-22-22-20000-222-20000000000000000000-2200000
χ592-2-22-2-2222-200002-22-2-22-2-222000000-22-22-2-2000000002200000000-22-22-22-2200002-2-220000000000000000000-2200000
χ602-2-22-2-2222-200002-22-2-22-2-222000000-22-22-2-2000000002200000000-22-22-22-220000-222-200000000000000000002-200000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-40000000022-2-2-2-222222200000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24400000000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ634444-4-4-4-44-40000-444444-4-4-4-40000000000-4400000000-4400000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-2400004-4-4-2-2-222220044-4-40000-2200000000-22-2-2-2-22222000000000000000000000000000000000000000000
χ654444-4-4-4-4-2400004-4-4-2-2-2222200-4-4440000-2200000000-222222-2-2-2-2000000000000000000000000000000000000000000
χ664444-4-4-4-4-2-40000-444-2-2-2222200000000002-2000000002-200000000−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000
χ674444-4-4-4-4-2-40000-444-2-2-2222200000000002-2000000002-2000000002i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000
χ6844-4-44-44-4-204i4i−4i−4i000-222-22-220022−2222−22−2i2−2i22i22i200−2i−2i2i2i000000−2−222−2−222i2i2i2i2−i2−i2−i2−i20000000000000000000000000000000000
χ6944-4-44-44-4-204i4i−4i−4i000-222-22-2200−2222−22222i22i2−2i2−2i200−2i−2i2i2i00000022−2−222−2−2−i2−i2−i2−i2i2i2i2i20000000000000000000000000000000000
χ7044-4-44-44-4-20−4i−4i4i4i000-222-22-220022−2222−222i22i2−2i2−2i2002i2i−2i−2i000000−2−222−2−222−i2−i2−i2−i2i2i2i2i20000000000000000000000000000000000
χ7144-4-44-44-4-20−4i−4i4i4i000-222-22-2200−2222−2222−2i2−2i22i22i2002i2i−2i−2i00000022−2−222−2−2i2i2i2i2−i2−i2−i2−i20000000000000000000000000000000000
χ7244-4-4-44-444000000004-4-4-44-440022−22−222200000000000000002222−22−22−22−222222000000000000000000000000000000000000000000
χ7344-4-4-44-444000000004-4-4-44-4400−222222−220000000000000000−22−2222222222−22−22000000000000000000000000000000000000000000
χ7444-4-4-44-44-200000000-2222-22-20022−22−2222000000000023−2323−2300−2−22222−2−26−6−66−666−60000000000000000000000000000000000
χ7544-4-4-44-44-200000000-2222-22-20022−22−22220000000000−2323−232300−2−22222−2−2−666−66−6−660000000000000000000000000000000000
χ7644-4-4-44-44-200000000-2222-22-200−222222−22000000000023−2323−230022−2−2−2−222−666−66−6−660000000000000000000000000000000000
χ7744-4-4-44-44-200000000-2222-22-200−222222−220000000000−2323−23230022−2−2−2−2226−6−66−666−60000000000000000000000000000000000
χ784-44-44-4-44404-4-44000-44-44-4-440000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ794-44-44-4-4440-444-4000-44-44-4-44000000000000-444-400000000000000000000000000000000000000000000000000000000
χ804-44-44-4-44-204-4-440002-22-222-2000000000000-222-20000006−6−666−6−6666−6−6−6−6660000000000000000000000000000000000
χ814-44-44-4-44-204-4-440002-22-222-2000000000000-222-2000000−666−6−666−6−6−66666−6−60000000000000000000000000000000000
χ824-44-44-4-44-20-444-40002-22-222-20000000000002-2-220000006−6−666−6−66−6−66666−6−60000000000000000000000000000000000
χ834-44-44-4-44-20-444-40002-22-222-20000000000002-2-22000000−666−6−666−666−6−6−6−6660000000000000000000000000000000000
χ844-44-4-444-4400000000-44-4-444-4000000−2i22i22i2−2i200000000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000
χ854-44-4-444-4400000000-44-4-444-40000002i2−2i2−2i22i2000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000
χ864-44-4-444-4-2000000002-222-2-22000000−2i22i22i2−2i2000000−2i32i32i3−2i3006−6−66−666−6i2−i2i2−i2−i2i2−i2i20000000000000000000000000000000000
χ874-44-4-444-4-2000000002-222-2-22000000−2i22i22i2−2i20000002i3−2i3−2i32i300−666−66−6−66i2−i2i2−i2−i2i2−i2i20000000000000000000000000000000000
χ884-44-4-444-4-2000000002-222-2-220000002i2−2i2−2i22i2000000−2i32i32i3−2i300−666−66−6−66−i2i2−i2i2i2−i2i2−i20000000000000000000000000000000000
χ894-44-4-444-4-2000000002-222-2-220000002i2−2i2−2i22i20000002i3−2i3−2i32i3006−6−66−666−6−i2i2−i2i2i2−i2i2−i20000000000000000000000000000000000
χ904-4-4444-4-4-2-44i−4i4i−4i44-422-2-2-222−4i4i000000002-2−2i2i−2i2i2i2i−2i−2i-2200000000000000000000000000000000000000000000000000
χ914-4-4444-4-4-2-4−4i4i−4i4i44-422-2-2-2224i−4i000000002-22i−2i2i−2i−2i−2i2i2i-2200000000000000000000000000000000000000000000000000
χ924-4-44-4-444440000-44-4-4-44-4-44400000000004400000000-4-400000000000000000000000000000000000000000000000000
χ934-4-44-4-444-240000-44-422-222-2-20000000000-2-2000000002223−2323−23−2323−2323000000000000000000000000000000000000000000
χ944-4-44-4-444-240000-44-422-222-2-20000000000-2-20000000022−2323−232323−2323−23000000000000000000000000000000000000000000
χ954-4-44-4-444-2-400004-4422-222-2-20000004-44-42200000000-2-200000000-22-22-22-220000000000000000000000000000000000
χ964-4-44-4-444-2-400004-4422-222-2-2000000-44-442200000000-2-2000000002-22-22-22-20000000000000000000000000000000000

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