Finite Group Databasebeta

← Group #10863712

Character table — Group #10863712

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212122222444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-11-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1
χ911111111111111111111-1-11111111111-1-1-1-1111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-11111-1-111-1-1-1-1
χ1011111111111111111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ1111111111111111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-111-1-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11111111-1-1-1-111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111-1-111-1-111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-111-1-11111-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-11111-1-1-1-11-1-11
χ17222222222-2-2-2-222222222200000000-2-22222-2-22222-20000000000-2-200000000000022-2-2000000000000000-2000
χ18222222222-2-2-2-222222222200000000-2-22222-2-2-2-2-2-2-20000000000-2-2000000000000-2-2220000000000000002000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000000000022000000000000-2-2-2-20000000000000002000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-220000000000220000000000002222000000000000000-2000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-2221111-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-21111-1-1111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-11111-1-10000-2-2-222-2-2-1-1-1-1111111-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000-2-2-2-2-222-1-1-1-11111111111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-2222222111111-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ29222-22-2-2-22-2-2222-22-2-2-22002i2i−2i−2i2i2i−2i−2i2-200002-200000002-2002i2i−2i−2i0000002i2i−2i−2i0000000000000002-20000000000
χ30222-22-2-2-22-2-2222-22-2-2-22002i2i−2i−2i−2i−2i2i2i2-200002-20000000-22002i2i−2i−2i000000−2i−2i2i2i000000000000000-220000000000
χ31222-22-2-2-22-2-2222-22-2-2-2200−2i−2i2i2i2i2i−2i−2i2-200002-20000000-2200−2i−2i2i2i0000002i2i−2i−2i000000000000000-220000000000
χ32222-22-2-2-22-2-2222-22-2-2-2200−2i−2i2i2i−2i−2i2i2i2-200002-200000002-200−2i−2i2i2i000000−2i−2i2i2i0000000000000002-20000000000
χ33222-22-2-2-2-1-2-222-11-1111-1002i2i−2i−2i2i2i−2i−2i-1133−3−3-1100000002-200−i−iii3−3−i3−i3i3i3−i−iii−i3−i3i3i30000000003−3-110000000000
χ34222-22-2-2-2-1-2-222-11-1111-1002i2i−2i−2i2i2i−2i−2i-11−3−333-1100000002-200−i−iii−33i3i3−i3−i3−i−iiii3i3−i3−i3000000000−33-110000000000
χ35222-22-2-2-2-1-2-222-11-1111-1002i2i−2i−2i−2i−2i2i2i-1133−3−3-110000000-2200−i−iii3−3−i3−i3i3i3ii−i−ii3i3−i3−i3000000000−331-10000000000
χ36222-22-2-2-2-1-2-222-11-1111-1002i2i−2i−2i−2i−2i2i2i-11−3−333-110000000-2200−i−iii−33i3i3−i3−i3ii−i−i−i3−i3i3i30000000003−31-10000000000
χ37222-22-2-2-2-1-2-222-11-1111-100−2i−2i2i2i2i2i−2i−2i-1133−3−3-110000000-2200ii−i−i3−3i3i3−i3−i3−i−iii−i3−i3i3i3000000000−331-10000000000
χ38222-22-2-2-2-1-2-222-11-1111-100−2i−2i2i2i2i2i−2i−2i-11−3−333-110000000-2200ii−i−i−33−i3−i3i3i3−i−iiii3i3−i3−i30000000003−31-10000000000
χ39222-22-2-2-2-1-2-222-11-1111-100−2i−2i2i2i−2i−2i2i2i-1133−3−3-1100000002-200ii−i−i3−3i3i3−i3−i3ii−i−ii3i3−i3−i30000000003−3-110000000000
χ40222-22-2-2-2-1-2-222-11-1111-100−2i−2i2i2i−2i−2i2i2i-11−3−333-1100000002-200ii−i−i−33−i3−i3i3i3ii−i−i−i3−i3i3i3000000000−33-110000000000
χ4122-2-2-22-222000022-22-2-2-22-200002−22−2002-22-2002i2i−2i−2i000002−200000000002−22−22−22−22i−2i00−i2−i2i2i2000000000000−i2i20
χ4222-2-2-22-222000022-22-2-2-22-200002−22−2002-22-200−2i−2i2i2i000002−200000000002−22−22−22−2−2i2i00i2i2−i2−i2000000000000i2−i20
χ4322-2-2-22-222000022-22-2-2-22-20000−22−22002-22-2002i2i−2i−2i00000−220000000000−22−22−22−222i−2i00i2i2−i2−i2000000000000i2−i20
χ4422-2-2-22-222000022-22-2-2-22-20000−22−22002-22-200−2i−2i2i2i00000−220000000000−22−22−22−22−2i2i00−i2−i2i2i2000000000000−i2i20
χ4522-2-2-22-222000022-22-2-2-2-2200002−22−200-22-22002i2i−2i−2i00000−2200000000002−22−2−22−22−2i2i00−i2−i2i2i2000000000000i2−i20
χ4622-2-2-22-222000022-22-2-2-2-2200002−22−200-22-2200−2i−2i2i2i00000−2200000000002−22−2−22−222i−2i00i2i2−i2−i2000000000000−i2i20
χ4722-2-2-22-222000022-22-2-2-2-220000−22−2200-22-22002i2i−2i−2i000002−20000000000−22−222−22−2−2i2i00i2i2−i2−i2000000000000−i2i20
χ4822-2-2-22-222000022-22-2-2-2-220000−22−2200-22-2200−2i−2i2i2i000002−20000000000−22−222−22−22i−2i00−i2−i2i2i2000000000000i2−i20
χ492-222-22-2-222-2-22-2-222-22-20000000000-2200002-22i−2i2i−2i02i−2i00000000002i−2i2i−2i00000000002i−2i000000000002-2000000
χ502-222-22-2-222-2-22-2-222-22-20000000000-2200002-22i−2i2i−2i0−2i2i0000000000−2i2i−2i2i00000000002i−2i00000000000-22000000
χ512-222-22-2-222-2-22-2-222-22-20000000000-2200002-2−2i2i−2i2i02i−2i00000000002i−2i2i−2i0000000000−2i2i00000000000-22000000
χ522-222-22-2-222-2-22-2-222-22-20000000000-2200002-2−2i2i−2i2i0−2i2i0000000000−2i2i−2i2i0000000000−2i2i000000000002-2000000
χ532-222-22-2-22-222-2-2-222-22-2002i−2i2i−2i00002-20000-222i−2i2i−2i00000002i−2i2i−2i0000000000000000−2i2i0000000002-200000000
χ542-222-22-2-22-222-2-2-222-22-2002i−2i2i−2i00002-20000-22−2i2i−2i2i00000002i−2i2i−2i00000000000000002i−2i000000000-2200000000
χ552-222-22-2-22-222-2-2-222-22-200−2i2i−2i2i00002-20000-222i−2i2i−2i0000000−2i2i−2i2i0000000000000000−2i2i000000000-2200000000
χ562-222-22-2-22-222-2-2-222-22-200−2i2i−2i2i00002-20000-22−2i2i−2i2i0000000−2i2i−2i2i00000000000000002i−2i0000000002-200000000
χ572-22-2-2-22222-22-2-222-22-2-2002-2-220000220000-2-2000000000002-2-220000000000000000002i−2i2i−2i0000000002i−2i0000
χ582-22-2-2-22222-22-2-222-22-2-2002-2-220000220000-2-2000000000002-2-22000000000000000000−2i2i−2i2i000000000−2i2i0000
χ592-22-2-2-22222-22-2-222-22-2-200-222-20000220000-2-200000000000-222-20000000000000000002i−2i2i−2i000000000−2i2i0000
χ602-22-2-2-22222-22-2-222-22-2-200-222-20000220000-2-200000000000-222-2000000000000000000−2i2i−2i2i0000000002i−2i0000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-2220000-400000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000000022222222000040000000000-2-200000000000000000000000000000000000
χ63444-44-4-4-4444-4-44-44-4-4-440000000000-440000-440000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-244-4-4-22-2222-200000000002-22323−23−232-2000000000000000−232300000000000000000000000000000000000
χ65444-44-4-4-4-244-4-4-22-2222-200000000002-2−23−2323232-200000000000000023−2300000000000000000000000000000000000
χ6644-44-4-44-4400004-4-4-444-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ6744-44-4-44-4400004-4-4-444-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ6844-44-4-44-4-20000-2222-2-22000000−2i22i22i2−2i20023−23−232300000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000
χ6944-44-4-44-4-20000-2222-2-22000000−2i22i22i2−2i200−232323−2300000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000
χ7044-44-4-44-4-20000-2222-2-220000002i2−2i2−2i22i20023−23−232300000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000
χ7144-44-4-44-4-20000-2222-2-220000002i2−2i2−2i22i200−232323−2300000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000
χ7244-4-4-44-44-20000-2-22-22224-4000022−2222−2200-22-220000000000022−220000000000−22−22−22−2200000000000000000000000
χ7344-4-4-44-44-20000-2-22-22224-40000−2222−222200-22-2200000000000−222200000000002−22−22−22−200000000000000000000000
χ7444-4-4-44-44-20000-2-22-2222-44000022−2222−22002-22-200000000000−22220000000000−22−222−22−200000000000000000000000
χ7544-4-4-44-44-20000-2-22-2222-440000−2222−2222002-22-20000000000022−2200000000002−22−2−22−2200000000000000000000000
χ764-444-44-4-4-24-4-4422-2-22-2200000000002-20000-22000004i−4i0000000000−2i2i−2i2i0000000000000000000000000000000
χ774-444-44-4-4-24-4-4422-2-22-2200000000002-20000-2200000−4i4i00000000002i−2i2i−2i0000000000000000000000000000000
χ784-444-44-4-4-2-444-422-2-22-22004i−4i4i−4i0000-2200002-200000000000−2i2i−2i2i0000000000000000000000000000000000000
χ794-444-44-4-4-2-444-422-2-22-2200−4i4i−4i4i0000-2200002-2000000000002i−2i2i−2i0000000000000000000000000000000000000
χ804-44-4-4-4444-44-44-444-44-4-40000000000-4-40000440000000000000000000000000000000000000000000000000000
χ814-44-4-4-444-24-44-42-2-22-222004-4-440000-2-200002200000000000-222-20000000000000000000000000000000000000
χ824-44-4-4-444-24-44-42-2-22-22200-444-40000-2-2000022000000000002-2-220000000000000000000000000000000000000
χ834-44-4-4-444-2-44-442-2-22-2220000000000220000-2-20000000000000000023−23−23230000000000000000000000000000000
χ844-44-4-4-444-2-44-442-2-22-2220000000000220000-2-200000000000000000−232323−230000000000000000000000000000000
χ854-4-444-4-4440000-44-4-4-44400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ864-4-444-4-4440000-44-4-4-444000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ874-4-4-4444-440000-4-4-444-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ884-4-4-4444-440000-4-4-444-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ898-8-888-8-88-400004-4444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-8888-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000

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