Finite Group Databasebeta

← Group #10829220

Character table — Group #10829220

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order1222222234444666666644444488881212121212121212444424444668812121212121212122424242424242424224488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-111-1-111-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-11-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111-1-1-1-111-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11111111-1-111-1-1111-1-1-1
χ911111111111111111111-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111-1-1-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-11111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-111-1-1111-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-22222-20000-2-200000000000000000022-2-20000000000000-200000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-2-20000-2-2000000000000000000-2-2220000000000000200000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222222000022000000000000000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-2200002200000000000000000022220000000000000-200000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000022222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-1-1-2-2-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-2-22211-2-21111-1-1-1-1-1-1-1-1111100000000-211-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-211221111-1-1-1-11111-1-1-1-1000000002-1-1110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-100002-2-2-2-2-1-12211111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-1-1-2-21111111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-222-2-211-2-2-1-1-1-11111-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-222221122-1-1-1-111111111-1-1-1-100000000-211-1-10000000000
χ29222-2-2-2-222-22-2222-22-2-2-22i2i−2i−2i0022-2-2-2-200002200000002i−2i000000002i2i−2i−2i22-2-20000000000000002i−2i0000000000
χ30222-2-2-2-222-22-2222-22-2-2-22i2i−2i−2i00-2-222-2-20000220000000−2i2i000000002i2i−2i−2i-2-222000000000000000−2i2i0000000000
χ31222-2-2-2-222-22-2222-22-2-2-2−2i−2i2i2i0022-2-2-2-20000220000000−2i2i00000000−2i−2i2i2i22-2-2000000000000000−2i2i0000000000
χ32222-2-2-2-222-22-2222-22-2-2-2−2i−2i2i2i00-2-222-2-200002200000002i−2i00000000−2i−2i2i2i-2-2220000000000000002i−2i0000000000
χ33222-2-2-2-22-1-22-22-1-11-11112i2i−2i−2i0022-2-211−i3−i3i3i3-1-100000002i−2i−i3i30033−3−3−i−iii-1-111−i3−i3i3i30000000003−3−ii0000000000
χ34222-2-2-2-22-1-22-22-1-11-11112i2i−2i−2i0022-2-211i3i3−i3−i3-1-100000002i−2ii3−i300−3−333−i−iii-1-111i3i3−i3−i3000000000−33−ii0000000000
χ35222-2-2-2-22-1-22-22-1-11-11112i2i−2i−2i00-2-22211−i3−i3i3i3-1-10000000−2i2i−i3i30033−3−3−i−iii11-1-1i3i3−i3−i3000000000−33i−i0000000000
χ36222-2-2-2-22-1-22-22-1-11-11112i2i−2i−2i00-2-22211i3i3−i3−i3-1-10000000−2i2ii3−i300−3−333−i−iii11-1-1−i3−i3i3i30000000003−3i−i0000000000
χ37222-2-2-2-22-1-22-22-1-11-1111−2i−2i2i2i0022-2-211−i3−i3i3i3-1-10000000−2i2i−i3i300−3−333ii−i−i-1-111−i3−i3i3i3000000000−33i−i0000000000
χ38222-2-2-2-22-1-22-22-1-11-1111−2i−2i2i2i0022-2-211i3i3−i3−i3-1-10000000−2i2ii3−i30033−3−3ii−i−i-1-111i3i3−i3−i30000000003−3i−i0000000000
χ39222-2-2-2-22-1-22-22-1-11-1111−2i−2i2i2i00-2-22211−i3−i3i3i3-1-100000002i−2i−i3i300−3−333ii−i−i11-1-1i3i3−i3−i30000000003−3−ii0000000000
χ40222-2-2-2-22-1-22-22-1-11-1111−2i−2i2i2i00-2-22211i3i3−i3−i3-1-100000002i−2ii3−i30033−3−3ii−i−i11-1-1−i3−i3i3i3000000000−33−ii0000000000
χ4122-2-2-222-2200002-22-2-2-2200002i−2i2−22−2002i−2i2i−2i002i2i−2i−2i0000000−i2i2000000002−22−2−i2i2−i2i22-200−i2−i2i2i20000000000002−20
χ4222-2-2-222-2200002-22-2-2-2200002i−2i2−22−2002i−2i2i−2i00−2i−2i2i2i0000000−i2i2000000002−22−2−i2i2−i2i2-2200i2i2−i2−i2000000000000−220
χ4322-2-2-222-2200002-22-2-2-2200002i−2i−22−22002i−2i2i−2i002i2i−2i−2i0000000i2−i200000000−22−22i2−i2i2−i22-200i2i2−i2−i2000000000000−220
χ4422-2-2-222-2200002-22-2-2-2200002i−2i−22−22002i−2i2i−2i00−2i−2i2i2i0000000i2−i200000000−22−22i2−i2i2−i2-2200−i2−i2i2i20000000000002−20
χ4522-2-2-222-2200002-22-2-2-220000−2i2i2−22−200−2i2i−2i2i002i2i−2i−2i0000000i2−i2000000002−22−2i2−i2i2−i2-2200−i2−i2i2i2000000000000−220
χ4622-2-2-222-2200002-22-2-2-220000−2i2i2−22−200−2i2i−2i2i00−2i−2i2i2i0000000i2−i2000000002−22−2i2−i2i2−i22-200i2i2−i2−i20000000000002−20
χ4722-2-2-222-2200002-22-2-2-220000−2i2i−22−2200−2i2i−2i2i002i2i−2i−2i0000000−i2i200000000−22−22−i2i2−i2i2-2200i2i2−i2−i20000000000002−20
χ4822-2-2-222-2200002-22-2-2-220000−2i2i−22−2200−2i2i−2i2i00−2i−2i2i2i0000000−i2i200000000−22−22−i2i2−i2i22-200−i2−i2i2i2000000000000−220
χ492-2-22-22-22222-2-2-2-2222-2-22i−2i2i−2i0000002-200002-2000000000000000002i−2i2i−2i0000000000002i−2i2i−2i00000000002-2000
χ502-2-22-22-22222-2-2-2-2222-2-22i−2i2i−2i0000002-200002-2000000000000000002i−2i2i−2i000000000000−2i2i−2i2i0000000000-22000
χ512-2-22-22-22222-2-2-2-2222-2-2−2i2i−2i2i0000002-200002-200000000000000000−2i2i−2i2i0000000000002i−2i2i−2i0000000000-22000
χ522-2-22-22-22222-2-2-2-2222-2-2−2i2i−2i2i0000002-200002-200000000000000000−2i2i−2i2i000000000000−2i2i−2i2i00000000002-2000
χ532-2-2-22-22222-2-22-2-2-22-22200000000002-20000-222-22-202-20000002-22-2000000000000002-20000000002-200000000
χ542-2-2-22-22222-2-22-2-2-22-22200000000002-20000-222-22-20-22000000-22-22000000000000002-2000000000-2200000000
χ552-2-2-22-22222-2-22-2-2-22-22200000000002-20000-22-22-2202-20000002-22-200000000000000-22000000000-2200000000
χ562-2-2-22-22222-2-22-2-2-22-22200000000002-20000-22-22-220-22000000-22-2200000000000000-220000000002-200000000
χ572-2-2-22-2222-222-2-2-2-22-2222-2-22000000-2200002-22-22-200000000000002-2-220000000000-22000000000002-2000000
χ582-2-2-22-2222-222-2-2-2-22-2222-2-22000000-2200002-2-22-2200000000000002-2-2200000000002-200000000000-22000000
χ592-2-2-22-2222-222-2-2-2-22-222-222-2000000-2200002-22-22-20000000000000-222-20000000000-2200000000000-22000000
χ602-2-2-22-2222-222-2-2-2-22-222-222-2000000-2200002-2-22-220000000000000-222-200000000002-2000000000002-2000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-2220000-400002200000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000040000-2-200000000000000000000000000000000000000000
χ63444-4-4-4-4444-44-444-44-4-4-40000000000440000-4-40000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44-24-44-4-2-22-22220000000000-2-2−2i3−2i32i32i3220000000002i3−2i300000000000000000000000000000000000000000
χ65444-4-4-4-44-24-44-4-2-22-22220000000000-2-22i32i3−2i3−2i322000000000−2i32i300000000000000000000000000000000000000000
χ6644-444-4-4-4400004-4-4-444-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ6744-444-4-4-4400004-4-4-444-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ6844-444-4-4-4-20000-2222-2-2200000022−22−22220023−23−232300000000000000000000000−222−2−666−600000000000000000000000
χ6944-444-4-4-4-20000-2222-2-2200000022−22−222200−232323−2300000000000000000000000−222−26−6−6600000000000000000000000
χ7044-444-4-4-4-20000-2222-2-22000000−222222−220023−23−2323000000000000000000000002−2−226−6−6600000000000000000000000
χ7144-444-4-4-4-20000-2222-2-22000000−222222−2200−232323−23000000000000000000000002−2−22−666−600000000000000000000000
χ7244-4-4-444-4-20000-22-2222-200004i−4i22−2222−2200−2i2i−2i2i0000000000000−2i22i200000000−22−22i2−i2i2−i200000000000000000000000
χ7344-4-4-444-4-20000-22-2222-200004i−4i−2222−222200−2i2i−2i2i00000000000002i2−2i2000000002−22−2−i2i2−i2i200000000000000000000000
χ7444-4-4-444-4-20000-22-2222-20000−4i4i22−2222−22002i−2i2i−2i00000000000002i2−2i200000000−22−22−i2i2−i2i200000000000000000000000
χ7544-4-4-444-4-20000-22-2222-20000−4i4i−2222−2222002i−2i2i−2i0000000000000−2i22i2000000002−22−2i2−i2i2−i200000000000000000000000
χ764-444-4-44-440000-44-4-44-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ774-444-4-44-440000-44-4-44-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ784-44-444-4-440000-444-4-44-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ794-44-444-4-440000-444-4-44-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ804-4-44-44-444-4-444-4-4444-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ814-4-44-44-44-244-4-422-2-2-2224i−4i4i−4i000000-220000-2200000000000000000−2i2i−2i2i0000000000000000000000000000000
χ824-4-44-44-44-244-4-422-2-2-222−4i4i−4i4i000000-220000-22000000000000000002i−2i2i−2i0000000000000000000000000000000
χ834-4-44-44-44-2-4-44422-2-2-22200000000002-200002-2000000000000023−23−232300000000000000000000000000000000000
χ844-4-44-44-44-2-4-44422-2-2-22200000000002-200002-20000000000000−232323−2300000000000000000000000000000000000
χ854-4-4-44-444-24-4-44222-22-2-20000000000-2200002-2000004-4000000-22-2200000000000000000000000000000000000
χ864-4-4-44-444-24-4-44222-22-2-20000000000-2200002-200000-440000002-22-200000000000000000000000000000000000
χ874-4-4-44-444-2-444-4222-22-2-24-4-440000002-20000-2200000000000000000-222-20000000000000000000000000000000
χ884-4-4-44-444-2-444-4222-22-2-2-444-40000002-20000-22000000000000000002-2-220000000000000000000000000000000
χ898-888-8-88-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-888-8-8-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000

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