Finite Group Databasebeta

← Group #10854243

Character table — Group #10854243

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-111-1-111-111-1-1-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11-1-111111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-11111-1-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-111-1-111111-1-1-1
χ911111111111111111111-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-111-1-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-11111111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-111-1-1111-1-1-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-22222-2000000-2-20000000000000000-2-22200000000000-20000000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-2-2000000-2-2000000000000000022-2-20000000000020000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222222000000220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-22000000220000000000000000222200000000000-20000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-222-2-2-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-2-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-2222222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ29222-22-2-2-2222-2-22-22-22-2-222-2-2000000220000-2-222-2-200000000022-2-20000000000002-2000000000002-200000000
χ30222-22-2-2-2222-2-22-22-22-2-222-2-2000000220000-2-2-2-22200000000022-2-2000000000000-2200000000000-2200000000
χ31222-22-2-2-2222-2-22-22-22-2-2-2-222000000220000-2-222-2-2000000000-2-2220000000000002-200000000000-2200000000
χ32222-22-2-2-2222-2-22-22-22-2-2-2-222000000220000-2-2-2-222000000000-2-222000000000000-22000000000002-200000000
χ33222-22-2-2-22-2-2222-22-22-2-20000000000-2-200002222-2-20002i−2i000000002i2i−2i−2i00000000-2200000000000000002i−2i000
χ34222-22-2-2-22-2-2222-22-22-2-20000000000-2-200002222-2-2000−2i2i00000000−2i−2i2i2i00000000-220000000000000000−2i2i000
χ35222-22-2-2-22-2-2222-22-22-2-20000000000-2-2000022-2-2220002i−2i000000002i2i−2i−2i000000002-20000000000000000−2i2i000
χ36222-22-2-2-22-2-2222-22-22-2-20000000000-2-2000022-2-222000−2i2i00000000−2i−2i2i2i000000002-200000000000000002i−2i000
χ3722-22-22-2-222-2-22-2-222-22-22i−2i2i−2i0000002-200002-200000000000002i−2i2i−2i000000000000000022-2-2000000002i−2i00000
χ3822-22-22-2-222-2-22-2-222-22-22i−2i2i−2i0000002-200002-200000000000002i−2i2i−2i0000000000000000-2-22200000000−2i2i00000
χ3922-22-22-2-222-2-22-2-222-22-2−2i2i−2i2i0000002-200002-20000000000000−2i2i−2i2i000000000000000022-2-200000000−2i2i00000
χ4022-22-22-2-222-2-22-2-222-22-2−2i2i−2i2i0000002-200002-20000000000000−2i2i−2i2i0000000000000000-2-222000000002i−2i00000
χ4122-2-2-2-22222-22-2-222-2-2-222i−2i−2i2i0022-2-22-20000-22000002i−2i0000002i−2i−2i2i000022-2-200000000000002i−2i000000000000
χ4222-2-2-2-22222-22-2-222-2-2-222i−2i−2i2i00-2-2222-20000-2200000−2i2i0000002i−2i−2i2i0000-2-2220000000000000−2i2i000000000000
χ4322-2-2-2-22222-22-2-222-2-2-22−2i2i2i−2i0022-2-22-20000-2200000−2i2i000000−2i2i2i−2i000022-2-20000000000000−2i2i000000000000
χ4422-2-2-2-22222-22-2-222-2-2-22−2i2i2i−2i00-2-2222-20000-22000002i−2i000000−2i2i2i−2i0000-2-22200000000000002i−2i000000000000
χ4522-2-2-2-222-12-22-21-1-1111-12i−2i−2i2i0022-2-2-1133−3−31-1000002i−2i00003−3−iii−i−i3i3−i3i3-1-11133−3−3000000000−ii−i3i30000000000
χ4622-2-2-2-222-12-22-21-1-1111-12i−2i−2i2i0022-2-2-11−3−3331-1000002i−2i0000−33−iii−ii3−i3i3−i3-1-111−3−333000000000−iii3−i30000000000
χ4722-2-2-2-222-12-22-21-1-1111-12i−2i−2i2i00-2-222-1133−3−31-100000−2i2i00003−3−iii−i−i3i3−i3i311-1-1−3−333000000000i−ii3−i30000000000
χ4822-2-2-2-222-12-22-21-1-1111-12i−2i−2i2i00-2-222-11−3−3331-100000−2i2i0000−33−iii−ii3−i3i3−i311-1-133−3−3000000000i−i−i3i30000000000
χ4922-2-2-2-222-12-22-21-1-1111-1−2i2i2i−2i0022-2-2-1133−3−31-100000−2i2i00003−3i−i−iii3−i3i3−i3-1-11133−3−3000000000i−ii3−i30000000000
χ5022-2-2-2-222-12-22-21-1-1111-1−2i2i2i−2i0022-2-2-11−3−3331-100000−2i2i0000−33i−i−ii−i3i3−i3i3-1-111−3−333000000000i−i−i3i30000000000
χ5122-2-2-2-222-12-22-21-1-1111-1−2i2i2i−2i00-2-222-1133−3−31-1000002i−2i00003−3i−i−iii3−i3i3−i311-1-1−3−333000000000−ii−i3i30000000000
χ5222-2-2-2-222-12-22-21-1-1111-1−2i2i2i−2i00-2-222-11−3−3331-1000002i−2i0000−33i−i−ii−i3i3−i3i311-1-133−3−3000000000−iii3−i30000000000
χ532-222-2-22-2200002-2-22-2-2200002i−2i2−22−2002i−2i2i−2i002i−2i2i−2i00000−i2i200000000002−22−2−i2i2−i2i2002-2−i2i2−i2i20000000000002−20
χ542-222-2-22-2200002-2-22-2-2200002i−2i2−22−2002i−2i2i−2i00−2i2i−2i2i00000−i2i200000000002−22−2−i2i2−i2i200-22i2−i2i2−i2000000000000−220
χ552-222-2-22-2200002-2-22-2-2200002i−2i−22−22002i−2i2i−2i002i−2i2i−2i00000i2−i20000000000−22−22i2−i2i2−i2002-2i2−i2i2−i2000000000000−220
χ562-222-2-22-2200002-2-22-2-2200002i−2i−22−22002i−2i2i−2i00−2i2i−2i2i00000i2−i20000000000−22−22i2−i2i2−i200-22−i2i2−i2i20000000000002−20
χ572-222-2-22-2200002-2-22-2-220000−2i2i2−22−200−2i2i−2i2i002i−2i2i−2i00000i2−i200000000002−22−2i2−i2i2−i200-22−i2i2−i2i2000000000000−220
χ582-222-2-22-2200002-2-22-2-220000−2i2i2−22−200−2i2i−2i2i00−2i2i−2i2i00000i2−i200000000002−22−2i2−i2i2−i2002-2i2−i2i2−i20000000000002−20
χ592-222-2-22-2200002-2-22-2-220000−2i2i−22−2200−2i2i−2i2i002i−2i2i−2i00000−i2i20000000000−22−22−i2i2−i2i200-22i2−i2i2−i20000000000002−20
χ602-222-2-22-2200002-2-22-2-220000−2i2i−22−2200−2i2i−2i2i00−2i2i−2i2i00000−i2i20000000000−22−22−i2i2−i2i2002-2−i2i2−i2i2000000000000−220
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-2220000-400000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-400002222222200004000000-2-2000000000000000000000000000000000000000
χ63444-44-4-4-4-244-4-4-22-22-22244-4-4000000-2-20000220000000000000-2-22200000000000000000000000000000000000
χ64444-44-4-4-4-244-4-4-22-22-222-4-444000000-2-2000022000000000000022-2-200000000000000000000000000000000000
χ65444-44-4-4-4-2-4-444-22-22-2220000000000220000-2-200000004i−4i00000000−2i−2i2i2i0000000000000000000000000000000
χ66444-44-4-4-4-2-4-444-22-22-2220000000000220000-2-20000000−4i4i000000002i2i−2i−2i0000000000000000000000000000000
χ6744-44-44-4-44-444-4-4-444-44-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ6844-44-44-4-4-24-4-4422-2-22-224i−4i4i−4i000000-220000-220000000000000−2i2i−2i2i00000000000000000000000000000000000
χ6944-44-44-4-4-24-4-4422-2-22-22−4i4i−4i4i000000-220000-2200000000000002i−2i2i−2i00000000000000000000000000000000000
χ7044-44-44-4-4-2-444-422-2-22-2200000000002-200002-20000000000000000023−23−23230000000000000000000000000000000
χ7144-44-44-4-4-2-444-422-2-22-2200000000002-200002-200000000000000000−232323−230000000000000000000000000000000
χ7244-4-4-4-4444-44-44-444-4-4-440000000000-4400004-40000000000000000000000000000000000000000000000000000
χ7344-4-4-4-444-2-44-442-2-2222-200000000002-22323−23−23-2200000000000−2323000000000000000000000000000000000000000
χ7444-4-4-4-444-2-44-442-2-2222-200000000002-2−23−232323-220000000000023−23000000000000000000000000000000000000000
χ754-444-4-44-4-20000-222-222-200004i−4i22−2222−2200−2i2i−2i2i00000000000−2i22i20000000000−22−22i2−i2i2−i200000000000000000000000
χ764-444-4-44-4-20000-222-222-200004i−4i−2222−222200−2i2i−2i2i000000000002i2−2i200000000002−22−2−i2i2−i2i200000000000000000000000
χ774-444-4-44-4-20000-222-222-20000−4i4i22−2222−22002i−2i2i−2i000000000002i2−2i20000000000−22−22−i2i2−i2i200000000000000000000000
χ784-444-4-44-4-20000-222-222-20000−4i4i−2222−2222002i−2i2i−2i00000000000−2i22i200000000002−22−2i2−i2i2−i200000000000000000000000
χ794-44-4-44-444000044-4-4-44-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ804-44-4-44-444000044-4-4-44-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ814-4-444-4-4440000-44-444-4-4000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ824-4-444-4-4440000-44-444-4-40000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ834-4-4-4444-440000-4-4-4-444400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ844-4-4-4444-440000-4-4-4-4444000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ854-4-4-4444-4-200002222-2-2-200000022−22−222200−2i32i32i3−2i300000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ864-4-4-4444-4-200002222-2-2-200000022−22−2222002i3−2i3−2i32i300000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ874-4-4-4444-4-200002222-2-2-2000000−222222−2200−2i32i32i3−2i3000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ884-4-4-4444-4-200002222-2-2-2000000−222222−22002i3−2i3−2i32i3000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ898-88-8-88-88-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-8-88-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000

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