Finite Group Databasebeta

← Group #10867924

Character table — Group #10867924

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424224488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ911111111111111111111-1-111111111111-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-111-1-111-111-1-1-1-1-1
χ1011111111111111111111-1-111111111111-1-1-1-11-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11-1-111111
χ1111111111111111111111-1-11111-1-1-1-1111-1-1-1-111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-111-1-1-111-1-1111
χ1211111111111111111111-1-11111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-111111-1-111-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111111-1-1-1-111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11-1-11111111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-1-111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-111-1-1-1-1111-1-1-1-11
χ17222222222-2-2-2-222222222200000000-2-2-22222-22222-2000000-2-2000000000000000022-2-200000000000-20000000
χ18222222222-2-2-2-222222222200000000-2-2-22222-2-2-2-2-2-2000000-2-20000000000000000-2-2220000000000020000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000000220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-22000000220000000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-1-11111-10000-222-2-2-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-11111-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-11111-10000-2-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1-11111-10000-2222222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ29222-2-2-2-2220000-22-2-222-22i−2i000022−2−20002i2i−2i−2i02i2i−2i−2i00000−i2i2000000000022−2−2−i2−i2i2i22-200−i2−i2i2i20000000000002−20
χ30222-2-2-2-2220000-22-2-222-22i−2i000022−2−20002i2i−2i−2i0−2i−2i2i2i00000−i2i2000000000022−2−2−i2−i2i2i2-2200i2i2−i2−i2000000000000−220
χ31222-2-2-2-2220000-22-2-222-22i−2i0000−2−2220002i2i−2i−2i02i2i−2i−2i00000i2−i20000000000−2−222i2i2−i2−i22-200i2i2−i2−i2000000000000−220
χ32222-2-2-2-2220000-22-2-222-22i−2i0000−2−2220002i2i−2i−2i0−2i−2i2i2i00000i2−i20000000000−2−222i2i2−i2−i2-2200−i2−i2i2i20000000000002−20
χ33222-2-2-2-2220000-22-2-222-2−2i2i000022−2−2000−2i−2i2i2i02i2i−2i−2i00000i2−i2000000000022−2−2i2i2−i2−i2-2200−i2−i2i2i2000000000000−220
χ34222-2-2-2-2220000-22-2-222-2−2i2i000022−2−2000−2i−2i2i2i0−2i−2i2i2i00000i2−i2000000000022−2−2i2i2−i2−i22-200i2i2−i2−i20000000000002−20
χ35222-2-2-2-2220000-22-2-222-2−2i2i0000−2−222000−2i−2i2i2i02i2i−2i−2i00000−i2i20000000000−2−222−i2−i2i2i2-2200i2i2−i2−i20000000000002−20
χ36222-2-2-2-2220000-22-2-222-2−2i2i0000−2−222000−2i−2i2i2i0−2i−2i2i2i00000−i2i20000000000−2−222−i2−i2i2i22-200−i2−i2i2i2000000000000−220
χ3722-2-2-222-22-222-2-2222-2-2-2002i2i−2i−2i2-22-22-2-200002000002i−2i0000002i2i−2i−2i00002-22-200000000000002i−2i000000000000
χ3822-2-2-222-22-222-2-2222-2-2-2002i2i−2i−2i-22-222-2-20000200000−2i2i0000002i2i−2i−2i0000-22-220000000000000−2i2i000000000000
χ3922-2-2-222-22-222-2-2222-2-2-200−2i−2i2i2i2-22-22-2-20000200000−2i2i000000−2i−2i2i2i00002-22-20000000000000−2i2i000000000000
χ4022-2-2-222-22-222-2-2222-2-2-200−2i−2i2i2i-22-222-2-200002000002i−2i000000−2i−2i2i2i0000-22-2200000000000002i−2i000000000000
χ4122-2-2-222-2-1-222-21-1-1-1111002i2i−2i−2i2-22-2-111−i3i3−i3i3-1000002i−2i0000−i3i3−i−iii33−3−3-11-11−i3i3−i3i3000000000−ii3−30000000000
χ4222-2-2-222-2-1-222-21-1-1-1111002i2i−2i−2i2-22-2-111i3−i3i3−i3-1000002i−2i0000i3−i3−i−iii−3−333-11-11i3−i3i3−i3000000000−ii−330000000000
χ4322-2-2-222-2-1-222-21-1-1-1111002i2i−2i−2i-22-22-111−i3i3−i3i3-100000−2i2i0000−i3i3−i−iii33−3−31-11-1i3−i3i3−i3000000000i−i−330000000000
χ4422-2-2-222-2-1-222-21-1-1-1111002i2i−2i−2i-22-22-111i3−i3i3−i3-100000−2i2i0000i3−i3−i−iii−3−3331-11-1−i3i3−i3i3000000000i−i3−30000000000
χ4522-2-2-222-2-1-222-21-1-1-111100−2i−2i2i2i2-22-2-111−i3i3−i3i3-100000−2i2i0000−i3i3ii−i−i−3−333-11-11−i3i3−i3i3000000000i−i−330000000000
χ4622-2-2-222-2-1-222-21-1-1-111100−2i−2i2i2i2-22-2-111i3−i3i3−i3-100000−2i2i0000i3−i3ii−i−i33−3−3-11-11i3−i3i3−i3000000000i−i3−30000000000
χ4722-2-2-222-2-1-222-21-1-1-111100−2i−2i2i2i-22-22-111−i3i3−i3i3-1000002i−2i0000−i3i3ii−i−i−3−3331-11-1i3−i3i3−i3000000000−ii3−30000000000
χ4822-2-2-222-2-1-222-21-1-1-111100−2i−2i2i2i-22-22-111i3−i3i3−i3-1000002i−2i0000i3−i3ii−i−i33−3−31-11-1−i3i3−i3i3000000000−ii−330000000000
χ492-22-22-22-2222-2-2-2-22-22-220000000000-22-2000022i−2i2i−2i0002-2000000002-22-200000000002i−2i000000000000002i−2i000
χ502-22-22-22-2222-2-2-2-22-22-220000000000-22-2000022i−2i2i−2i000-2200000000-22-2200000000002i−2i00000000000000−2i2i000
χ512-22-22-22-2222-2-2-2-22-22-220000000000-22-200002−2i2i−2i2i0002-2000000002-22-20000000000−2i2i00000000000000−2i2i000
χ522-22-22-22-2222-2-2-2-22-22-220000000000-22-200002−2i2i−2i2i000-2200000000-22-220000000000−2i2i000000000000002i−2i000
χ532-22-22-22-22-2-222-2-22-22-22002i−2i2i−2i00002-220000-22i−2i2i−2i0000000002i−2i2i−2i00000000000000−2i2i0000000000002-200000
χ542-22-22-22-22-2-222-2-22-22-22002i−2i2i−2i00002-220000-2−2i2i−2i2i0000000002i−2i2i−2i000000000000002i−2i000000000000-2200000
χ552-22-22-22-22-2-222-2-22-22-2200−2i2i−2i2i00002-220000-22i−2i2i−2i000000000−2i2i−2i2i00000000000000−2i2i000000000000-2200000
χ562-22-22-22-22-2-222-2-22-22-2200−2i2i−2i2i00002-220000-2−2i2i−2i2i000000000−2i2i−2i2i000000000000002i−2i0000000000002-200000
χ572-2-22-2-22222-22-22-22-2-22-2002-2-22000022-20000-200000000000002-2-2200000000000000002i−2i2i−2i000002i−2i00000000
χ582-2-22-2-22222-22-22-22-2-22-2002-2-22000022-20000-200000000000002-2-220000000000000000−2i2i−2i2i00000−2i2i00000000
χ592-2-22-2-22222-22-22-22-2-22-200-222-2000022-20000-20000000000000-222-200000000000000002i−2i2i−2i00000−2i2i00000000
χ602-2-22-2-22222-22-22-22-2-22-200-222-2000022-20000-20000000000000-222-20000000000000000−2i2i−2i2i000002i−2i00000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000222-2-2-2-220000-400000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000000002222222200004000000-2-2000000000000000000000000000000000000000
χ63444-4-4-4-44-200002-222-2-224i−4i00002222−22−22000−2i−2i2i2i0000000000−2i22i20000000000−2−222i2i2−i2−i200000000000000000000000
χ64444-4-4-4-44-200002-222-2-224i−4i0000−22−222222000−2i−2i2i2i00000000002i2−2i2000000000022−2−2−i2−i2i2i200000000000000000000000
χ65444-4-4-4-44-200002-222-2-22−4i4i00002222−22−220002i2i−2i−2i00000000002i2−2i20000000000−2−222−i2−i2i2i200000000000000000000000
χ66444-4-4-4-44-200002-222-2-22−4i4i0000−22−2222220002i2i−2i−2i0000000000−2i22i2000000000022−2−2i2i2−i2−i200000000000000000000000
χ6744-444-4-4-44000044-4-4-4-4400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ6844-444-4-4-44000044-4-4-4-44000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ6944-444-4-4-4-20000-2-22222-200000022−22−222200023−23−23230000000000000000000000−222−2−666−600000000000000000000000
χ7044-444-4-4-4-20000-2-22222-200000022−22−2222000−232323−230000000000000000000000−222−26−6−6600000000000000000000000
χ7144-444-4-4-4-20000-2-22222-2000000−222222−2200023−23−232300000000000000000000002−2−226−6−6600000000000000000000000
χ7244-444-4-4-4-20000-2-22222-2000000−222222−22000−232323−2300000000000000000000002−2−22−666−600000000000000000000000
χ7344-4-4-444-444-4-44-4444-4-4-40000000000-4440000-40000000000000000000000000000000000000000000000000000
χ7444-4-4-444-4-24-4-442-2-2-222200000000002-2-2−2i32i3−2i32i32000000000002i3−2i3000000000000000000000000000000000000000
χ7544-4-4-444-4-24-4-442-2-2-222200000000002-2-22i3−2i32i3−2i3200000000000−2i32i3000000000000000000000000000000000000000
χ764-444-44-4-4400004-4-444-4-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ774-444-44-4-4400004-4-444-4-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ784-44-44-44-4-244-4-422-22-22-200000000002-220000-200000004-400000000-22-220000000000000000000000000000000
χ794-44-44-44-4-244-4-422-22-22-200000000002-220000-20000000-44000000002-22-20000000000000000000000000000000
χ804-44-44-44-4-2-4-44422-22-22-2004i−4i4i−4i0000-22-2000020000000000000−2i2i−2i2i00000000000000000000000000000000000
χ814-44-44-44-4-2-4-44422-22-22-200−4i4i−4i4i0000-22-20000200000000000002i−2i2i−2i00000000000000000000000000000000000
χ824-4-44-4-4444-44-444-44-4-44-40000000000-4-44000040000000000000000000000000000000000000000000000000000
χ834-4-44-4-444-24-44-4-22-222-22004-4-440000-2-22000020000000000000-222-200000000000000000000000000000000000
χ844-4-44-4-444-24-44-4-22-222-2200-444-40000-2-220000200000000000002-2-2200000000000000000000000000000000000
χ854-4-44-4-444-2-44-44-22-222-22000000000022-20000-20000000000000000023−23−23230000000000000000000000000000000
χ864-4-44-4-444-2-44-44-22-222-22000000000022-20000-200000000000000000−232323−230000000000000000000000000000000
χ874-4-4-444-4440000-4-4-44-44400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ884-4-4-444-4440000-4-4-44-444000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ898-888-88-8-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-88-40000444-44-4-40000000000000000000000000000000000000000000000000000000000000000000000

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