Finite Group Databasebeta

← Group #10945156

Character table — Group #10945156

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order1222222234444444466666664444444444121212121212121244444444888812121212121212121212242424242424242422224444444424661212888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111111111-1-1
χ911111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-111-1-111-1-1-11
χ1011111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-111-1-1111-1
χ1111111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-111-1-1-1-1111-1
χ1211111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-11-1-11111-1-1-11
χ1311111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-11-1-11111-1-11-1
χ1411111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-1-111-11
χ1511111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-111-11
χ1611111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111-111-1-111-1-11-1
χ17222222222-2-22222-2-22222222-2-200000000-2-22222-2-2222222220000-2-200000000000000000000-2-20000-2-2000000000000
χ18222222222-2-22222-2-22222222-2-200000000-2-22222-2-2-2-2-2-2-2-2-2-20000-2-20000000000000000000022000022000000000000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-22222-2-2-2-200002200000000000000000000-2-2000022000000000000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-2-2-2-2-2222200002200000000000000000000220000-2-2000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000000022-2-211-1-1-1-11111-1-1-1-111110000000000002-2-1-111000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-100000000-2-22211-1-1-1-111111111-1-1-1-1000000000000-2211-1-1000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000000022-2-2111111-1-1-1-1-1-1-1-11111000000000000-2211-1-1000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-100000000-2-222111111-1-1-1-11111-1-1-1-10000000000002-2-1-111000000
χ29222-2-2-22-222-200002-2-2222-2-2-20000002i2i−2i−2i2-200002-22i2i−2i−2i000000000000002i2i−2i−2i0000000000002i−2i22-2-200000000000000
χ30222-2-2-22-222-200002-2-2222-2-2-20000002i2i−2i−2i2-200002-2−2i−2i2i2i000000000000002i2i−2i−2i000000000000−2i2i-2-22200000000000000
χ31222-2-2-22-222-200002-2-2222-2-2-2000000−2i−2i2i2i2-200002-22i2i−2i−2i00000000000000−2i−2i2i2i0000000000002i−2i-2-22200000000000000
χ32222-2-2-22-222-200002-2-2222-2-2-2000000−2i−2i2i2i2-200002-2−2i−2i2i2i00000000000000−2i−2i2i2i000000000000−2i2i22-2-200000000000000
χ33222-2-2-22-22-220000-22-2222-2-2-2002i2i−2i−2i0000-220000-222i2i−2i−2i00000000002i2i−2i−2i00000000000022-2-2−2i2i000000000000000000
χ34222-2-2-22-22-220000-22-2222-2-2-2002i2i−2i−2i0000-220000-22−2i−2i2i2i00000000002i2i−2i−2i000000000000-2-2222i−2i000000000000000000
χ35222-2-2-22-22-220000-22-2222-2-2-200−2i−2i2i2i0000-220000-222i2i−2i−2i0000000000−2i−2i2i2i000000000000-2-222−2i2i000000000000000000
χ36222-2-2-22-22-220000-22-2222-2-2-200−2i−2i2i2i0000-220000-22−2i−2i2i2i0000000000−2i−2i2i2i00000000000022-2-22i−2i000000000000000000
χ3722-222-2-2-22002i2i−2i−2i0022-2-22-2-20000000000002i2i−2i−2i002i−2i2i−2i22-2-2−i2i22−20000000000−i2−i2i2i222−2−20000000000000000002−2−i2i200
χ3822-222-2-2-22002i2i−2i−2i0022-2-22-2-20000000000002i2i−2i−2i002i−2i2i−2i22-2-2i2−i2−220000000000i2i2−i2−i2−2−222000000000000000000−22i2−i200
χ3922-222-2-2-22002i2i−2i−2i0022-2-22-2-20000000000002i2i−2i−2i00−2i2i−2i2i-2-222−i2i22−20000000000−i2−i2i2i222−2−2000000000000000000−22i2−i200
χ4022-222-2-2-22002i2i−2i−2i0022-2-22-2-20000000000002i2i−2i−2i00−2i2i−2i2i-2-222i2−i2−220000000000i2i2−i2−i2−2−2220000000000000000002−2−i2i200
χ4122-222-2-2-2200−2i−2i2i2i0022-2-22-2-2000000000000−2i−2i2i2i002i−2i2i−2i-2-222−i2i2−220000000000−i2−i2i2i2−2−2220000000000000000002−2i2−i200
χ4222-222-2-2-2200−2i−2i2i2i0022-2-22-2-2000000000000−2i−2i2i2i002i−2i2i−2i-2-222i2−i22−20000000000i2i2−i2−i222−2−2000000000000000000−22−i2i200
χ4322-222-2-2-2200−2i−2i2i2i0022-2-22-2-2000000000000−2i−2i2i2i00−2i2i−2i2i22-2-2−i2i2−220000000000−i2−i2i2i2−2−222000000000000000000−22−i2i200
χ4422-222-2-2-2200−2i−2i2i2i0022-2-22-2-2000000000000−2i−2i2i2i00−2i2i−2i2i22-2-2i2−i22−20000000000i2i2−i2−i222−2−20000000000000000002−2i2−i200
χ452-222-22-2-222-22i−2i2i−2i-222-22-2-22-22i−2i000000002-22i−2i2i−2i-220000000000002i−2i00000000000000002-22-2002i−2i2i−2i00000000000000
χ462-222-22-2-222-22i−2i2i−2i-222-22-2-22-22i−2i000000002-22i−2i2i−2i-220000000000002i−2i0000000000000000-22-2200−2i2i−2i2i00000000000000
χ472-222-22-2-222-2−2i2i−2i2i-222-22-2-22-2−2i2i000000002-2−2i2i−2i2i-22000000000000−2i2i00000000000000002-22-200−2i2i−2i2i00000000000000
χ482-222-22-2-222-2−2i2i−2i2i-222-22-2-22-2−2i2i000000002-2−2i2i−2i2i-22000000000000−2i2i0000000000000000-22-22002i−2i2i−2i00000000000000
χ492-222-22-2-22-222i−2i2i−2i2-22-22-2-22-2−2i2i2-22-22i−2i2i−2i-222i−2i2i−2i2-2000000000000−2i2i2-22-22i−2i2i−2i00000000000000000000000000000000
χ502-222-22-2-22-222i−2i2i−2i2-22-22-2-22-2−2i2i-22-22−2i2i−2i2i-222i−2i2i−2i2-2000000000000−2i2i-22-22−2i2i−2i2i00000000000000000000000000000000
χ512-222-22-2-22-22−2i2i−2i2i2-22-22-2-22-22i−2i2-22-2−2i2i−2i2i-22−2i2i−2i2i2-20000000000002i−2i2-22-2−2i2i−2i2i00000000000000000000000000000000
χ522-222-22-2-22-22−2i2i−2i2i2-22-22-2-22-22i−2i-22-222i−2i2i−2i-22−2i2i−2i2i2-20000000000002i−2i-22-222i−2i2i−2i00000000000000000000000000000000
χ532-222-22-2-2-1-222i−2i2i−2i2-2-11-111-11−2i2i2-22-22i−2i2i−2i1-1−ii−ii-11000000000000i−i-11-11−ii−ii−i3i3−i3i33−33−300000000000000−i3i33−3000000
χ542-222-22-2-2-1-222i−2i2i−2i2-2-11-111-11−2i2i2-22-22i−2i2i−2i1-1−ii−ii-11000000000000i−i-11-11−ii−iii3−i3i3−i3−33−3300000000000000i3−i3−33000000
χ552-222-22-2-2-1-222i−2i2i−2i2-2-11-111-11−2i2i-22-22−2i2i−2i2i1-1−ii−ii-11000000000000i−i1-11-1i−ii−i−i3i3−i3i33−33−300000000000000i3−i3−33000000
χ562-222-22-2-2-1-222i−2i2i−2i2-2-11-111-11−2i2i-22-22−2i2i−2i2i1-1−ii−ii-11000000000000i−i1-11-1i−ii−ii3−i3i3−i3−33−3300000000000000−i3i33−3000000
χ572-222-22-2-2-1-22−2i2i−2i2i2-2-11-111-112i−2i2-22-2−2i2i−2i2i1-1i−ii−i-11000000000000−ii-11-11i−ii−i−i3i3−i3i3−33−3300000000000000−i3i3−33000000
χ582-222-22-2-2-1-22−2i2i−2i2i2-2-11-111-112i−2i2-22-2−2i2i−2i2i1-1i−ii−i-11000000000000−ii-11-11i−ii−ii3−i3i3−i33−33−300000000000000i3−i33−3000000
χ592-222-22-2-2-1-22−2i2i−2i2i2-2-11-111-112i−2i-22-222i−2i2i−2i1-1i−ii−i-11000000000000−ii1-11-1−ii−ii−i3i3−i3i3−33−3300000000000000i3−i33−3000000
χ602-222-22-2-2-1-22−2i2i−2i2i2-2-11-111-112i−2i-22-222i−2i2i−2i1-1i−ii−i-11000000000000−ii1-11-1−ii−iii3−i3i3−i33−33−300000000000000−i3i3−33000000
χ612-22-22-2-222220000-2-2-2-22-22-22002i−2i−2i2i0000220000-2-200002-22-20000002i−2i−2i2i0000000000000000002i−2i−2i2i2-2000000000000
χ622-22-22-2-222220000-2-2-2-22-22-22002i−2i−2i2i0000220000-2-20000-22-220000002i−2i−2i2i000000000000000000−2i2i2i−2i-22000000000000
χ632-22-22-2-222220000-2-2-2-22-22-2200−2i2i2i−2i0000220000-2-200002-22-2000000−2i2i2i−2i000000000000000000−2i2i2i−2i2-2000000000000
χ642-22-22-2-222220000-2-2-2-22-22-2200−2i2i2i−2i0000220000-2-20000-22-22000000−2i2i2i−2i0000000000000000002i−2i−2i2i-22000000000000
χ652-22-22-2-222-2-2000022-2-22-22-220000002-2-22-2-200002200002-22-200000000002-2-2200000000-222-2000000-22000000000000
χ662-22-22-2-222-2-2000022-2-22-22-220000002-2-22-2-20000220000-22-2200000000002-2-22000000002-2-220000002-2000000000000
χ672-22-22-2-222-2-2000022-2-22-22-22000000-222-2-2-200002200002-22-20000000000-222-2000000002-2-22000000-22000000000000
χ682-22-22-2-222-2-2000022-2-22-22-22000000-222-2-2-20000220000-22-220000000000-222-200000000-222-20000002-2000000000000
χ6944444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-40000000022-2-2-2-222000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022222222000000000000-2-20000000000000000000000000000000000000000
χ71444-4-4-44-4-24-400004-42-2-2-22220000004i4i−4i−4i-220000-22000000000000000000−2i−2i2i2i00000000000000000000000000000000
χ72444-4-4-44-4-24-400004-42-2-2-2222000000−4i−4i4i4i-220000-220000000000000000002i2i−2i−2i00000000000000000000000000000000
χ73444-4-4-44-4-2-440000-442-2-2-2222004i4i−4i−4i00002-200002-200000000000000−2i−2i2i2i000000000000000000000000000000000000
χ74444-4-4-44-4-2-440000-442-2-2-222200−4i−4i4i4i00002-200002-2000000000000002i2i−2i−2i000000000000000000000000000000000000
χ7544-444-4-4-4-2004i4i−4i−4i00-2-222-222000000000000−2i−2i2i2i0000000000−2i22i222−220000000000i2i2−i2−i2−2−222000000000000000000000000
χ7644-444-4-4-4-2004i4i−4i−4i00-2-222-222000000000000−2i−2i2i2i00000000002i2−2i2−22220000000000−i2−i2i2i222−2−2000000000000000000000000
χ7744-444-4-4-4-200−4i−4i4i4i00-2-222-2220000000000002i2i−2i−2i0000000000−2i22i2−22220000000000i2i2−i2−i222−2−2000000000000000000000000
χ7844-444-4-4-4-200−4i−4i4i4i00-2-222-2220000000000002i2i−2i−2i00000000002i2−2i222−220000000000−i2−i2i2i2−2−222000000000000000000000000
χ7944-4-4-44-44400000000-44-4-4-4440000000000000000004-4-4400000000000000000000000000000000000000000000000000
χ8044-4-4-44-44400000000-44-4-4-444000000000000000000-444-400000000000000000000000000000000000000000000000000
χ814-444-44-4-4-24-44i−4i4i−4i-44-22-222-224i−4i00000000-22−2i2i−2i2i2-2000000000000−2i2i0000000000000000000000000000000000000000
χ824-444-44-4-4-24-4−4i4i−4i4i-44-22-222-22−4i4i00000000-222i−2i2i−2i2-20000000000002i−2i0000000000000000000000000000000000000000
χ834-44-44-4-44-2440000-4-422-22-22-2004i−4i−4i4i0000-2-200002200000000000000−2i2i2i−2i000000000000000000000000000000000000
χ844-44-44-4-44-2440000-4-422-22-22-200−4i4i4i−4i0000-2-2000022000000000000002i−2i−2i2i000000000000000000000000000000000000
χ854-44-44-4-44-2-4-400004422-22-22-20000004-4-44220000-2-2000000000000000000-222-200000000000000000000000000000000
χ864-44-44-4-44-2-4-400004422-22-22-2000000-444-4220000-2-20000000000000000002-2-2200000000000000000000000000000000
χ874-4-44-4-4444004-4-44004-4-44-4-440000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ884-4-44-4-444400-444-4004-4-44-4-44000000000000-444-400000000000000000000000000000000000000000000000000000000
χ894-4-44-4-444-2004-4-4400-222-222-2000000000000-222-20000000000000000000000006−6−666−6−66000000000000000000000000
χ904-4-44-4-444-2004-4-4400-222-222-2000000000000-222-2000000000000000000000000−666−6−666−6000000000000000000000000
χ914-4-44-4-444-200-444-400-222-222-20000000000002-2-220000000000000000000000006−6−66−666−6000000000000000000000000
χ924-4-44-4-444-200-444-400-222-222-20000000000002-2-22000000000000000000000000−666−66−6−66000000000000000000000000
χ934-4-4-4444-4400000000-4-4-4444-400000000000000000000004-4-440000000000000000000000000000000000000000000000
χ944-4-4-4444-4400000000-4-4-4444-40000000000000000000000-444-40000000000000000000000000000000000000000000000
χ9588-8-8-88-88-4000000004-4444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-8888-8-400000000444-4-4-44000000000000000000000000000000000000000000000000000000000000000000000000

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