Finite Group Databasebeta

← Group #10854147

Character table — Group #10854147

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
χ311111111111111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-111-1-111-1-1-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1111-1-1111
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
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-111-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-111111-1-11111-1
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
χ29222-2-2-2-2222-22-22-22-2-2-222i2i−2i−2i0022-2-22-200002-2000002i−2i0000002i2i−2i−2i000022-2-200000000000002i−2i000000000000
χ30222-2-2-2-2222-22-22-22-2-2-222i2i−2i−2i00-2-2222-200002-200000−2i2i0000002i2i−2i−2i0000-2-2220000000000000−2i2i000000000000
χ31222-2-2-2-2222-22-22-22-2-2-22−2i−2i2i2i0022-2-22-200002-200000−2i2i000000−2i−2i2i2i000022-2-20000000000000−2i2i000000000000
χ32222-2-2-2-2222-22-22-22-2-2-22−2i−2i2i2i00-2-2222-200002-2000002i−2i000000−2i−2i2i2i0000-2-22200000000000002i−2i000000000000
χ33222-2-2-2-22-12-22-2-11-1111-12i2i−2i−2i0022-2-2-1133−3−3-11000002i−2i00003−3−i−iii−i3−i3i3i3-1-11133−3−3000000000−ii−i3i30000000000
χ34222-2-2-2-22-12-22-2-11-1111-12i2i−2i−2i0022-2-2-11−3−333-11000002i−2i0000−33−i−iiii3i3−i3−i3-1-111−3−333000000000−iii3−i30000000000
χ35222-2-2-2-22-12-22-2-11-1111-12i2i−2i−2i00-2-222-1133−3−3-1100000−2i2i00003−3−i−iii−i3−i3i3i311-1-1−3−333000000000i−ii3−i30000000000
χ36222-2-2-2-22-12-22-2-11-1111-12i2i−2i−2i00-2-222-11−3−333-1100000−2i2i0000−33−i−iiii3i3−i3−i311-1-133−3−3000000000i−i−i3i30000000000
χ37222-2-2-2-22-12-22-2-11-1111-1−2i−2i2i2i0022-2-2-1133−3−3-1100000−2i2i00003−3ii−i−ii3i3−i3−i3-1-11133−3−3000000000i−ii3−i30000000000
χ38222-2-2-2-22-12-22-2-11-1111-1−2i−2i2i2i0022-2-2-11−3−333-1100000−2i2i0000−33ii−i−i−i3−i3i3i3-1-111−3−333000000000i−i−i3i30000000000
χ39222-2-2-2-22-12-22-2-11-1111-1−2i−2i2i2i00-2-222-1133−3−3-11000002i−2i00003−3ii−i−ii3i3−i3−i311-1-1−3−333000000000−ii−i3i30000000000
χ40222-2-2-2-22-12-22-2-11-1111-1−2i−2i2i2i00-2-222-11−3−333-11000002i−2i0000−33ii−i−i−i3−i3i3i311-1-133−3−3000000000−iii3−i30000000000
χ412-222-22-2-2222-2-2-222-22-2-22-22-2000000220000-2-222-2-20000000002-22-20000000000002-2000000000002-200000000
χ422-222-22-2-2222-2-2-222-22-2-22-22-2000000220000-2-2-2-2220000000002-22-2000000000000-2200000000000-2200000000
χ432-222-22-2-2222-2-2-222-22-2-2-22-22000000220000-2-222-2-2000000000-22-220000000000002-200000000000-2200000000
χ442-222-22-2-2222-2-2-222-22-2-2-22-22000000220000-2-2-2-222000000000-22-22000000000000-22000000000002-200000000
χ452-222-22-2-22-2-222-222-22-2-20000000000-2-200002222-2-20002i−2i000000002i−2i2i−2i00000000-22000000000000002i−2i00000
χ462-222-22-2-22-2-222-222-22-2-20000000000-2-200002222-2-2000−2i2i00000000−2i2i−2i2i00000000-2200000000000000−2i2i00000
χ472-222-22-2-22-2-222-222-22-2-20000000000-2-2000022-2-2220002i−2i000000002i−2i2i−2i000000002-200000000000000−2i2i00000
χ482-222-22-2-22-2-222-222-22-2-20000000000-2-2000022-2-222000−2i2i00000000−2i2i−2i2i000000002-2000000000000002i−2i00000
χ492-22-22-22-222-2-22-2-222-22-22i−2i−2i2i0000002-20000-2200000000000002i−2i−2i2i000000000000000022-2-200000000002i−2i000
χ502-22-22-22-222-2-22-2-222-22-22i−2i−2i2i0000002-20000-2200000000000002i−2i−2i2i0000000000000000-2-2220000000000−2i2i000
χ512-22-22-22-222-2-22-2-222-22-2−2i2i2i−2i0000002-20000-220000000000000−2i2i2i−2i000000000000000022-2-20000000000−2i2i000
χ522-22-22-22-222-2-22-2-222-22-2−2i2i2i−2i0000002-20000-220000000000000−2i2i2i−2i0000000000000000-2-22200000000002i−2i000
χ532-2-2-2-222220000-2-2-2-222200002-22−22−2002-22-2002-22-2000002−200000000002−22−22−22−2002-22−22−20000000000002−20
χ542-2-2-2-222220000-2-2-2-222200002-22−22−2002-22-200-22-22000002−200000000002−22−22−22−200-22−22−22000000000000−220
χ552-2-2-2-222220000-2-2-2-222200002-2−22−22002-22-2002-22-200000−220000000000−22−22−22−22002-2−22−22000000000000−220
χ562-2-2-2-222220000-2-2-2-222200002-2−22−22002-22-200-22-2200000−220000000000−22−22−22−2200-222−22−20000000000002−20
χ572-2-2-2-222220000-2-2-2-22220000-222−22−200-22-22002-22-200000−2200000000002−22−2−22−2200-222−22−2000000000000−220
χ582-2-2-2-222220000-2-2-2-22220000-222−22−200-22-2200-22-2200000−2200000000002−22−2−22−22002-2−22−220000000000002−20
χ592-2-2-2-222220000-2-2-2-22220000-22−22−2200-22-22002-22-2000002−20000000000−22−222−22−200-22−22−220000000000002−20
χ602-2-2-2-222220000-2-2-2-22220000-22−22−2200-22-2200-22-22000002−20000000000−22−222−22−2002-22−22−2000000000000−220
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
χ63444-4-4-4-444-44-444-44-4-4-440000000000-440000-440000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44-2-44-44-22-2222-200000000002-22323−23−232-200000000000−2323000000000000000000000000000000000000000
χ65444-4-4-4-44-2-44-44-22-2222-200000000002-2−23−2323232-20000000000023−23000000000000000000000000000000000000000
χ6644-44-4-44-44000044-4-4-44-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ6744-44-4-44-44000044-4-4-44-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ6844-4-444-4-4400004-4-444-4-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ6944-4-444-4-4400004-4-444-4-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ704-444-44-4-4-244-4-42-2-22-2224-44-4000000-2-20000220000000000000-22-2200000000000000000000000000000000000
χ714-444-44-4-4-244-4-42-2-22-222-44-44000000-2-200002200000000000002-22-200000000000000000000000000000000000
χ724-444-44-4-4-2-4-4442-2-22-2220000000000220000-2-200000004i−4i00000000−2i2i−2i2i0000000000000000000000000000000
χ734-444-44-4-4-2-4-4442-2-22-2220000000000220000-2-20000000−4i4i000000002i−2i2i−2i0000000000000000000000000000000
χ744-44-44-44-44-444-4-4-444-44-40000000000-4400004-40000000000000000000000000000000000000000000000000000
χ754-44-44-44-4-24-4-4422-2-22-224i−4i−4i4i000000-2200002-20000000000000−2i2i2i−2i00000000000000000000000000000000000
χ764-44-44-44-4-24-4-4422-2-22-22−4i4i4i−4i000000-2200002-200000000000002i−2i−2i2i00000000000000000000000000000000000
χ774-44-44-44-4-2-444-422-2-22-2200000000002-20000-220000000000000000023−23−23230000000000000000000000000000000
χ784-44-44-44-4-2-444-422-2-22-2200000000002-20000-2200000000000000000−232323−230000000000000000000000000000000
χ794-4-444-4-4440000-44-44-4-4400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ804-4-444-4-4440000-44-44-4-44000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ814-4-444-4-44-200002-22-222-200000022−22−22220023−23−232300000000000000000000000−222−26−6−6600000000000000000000000
χ824-4-444-4-44-200002-22-222-200000022−22−222200−232323−2300000000000000000000000−222−2−666−600000000000000000000000
χ834-4-444-4-44-200002-22-222-2000000−222222−220023−23−2323000000000000000000000002−2−22−666−600000000000000000000000
χ844-4-444-4-44-200002-22-222-2000000−222222−2200−232323−23000000000000000000000002−2−226−6−6600000000000000000000000
χ854-4-4-4-4444-200002222-2-2-200004-422−2222−2200-22-220000000000022−220000000000−22−22−22−2200000000000000000000000
χ864-4-4-4-4444-200002222-2-2-200004-4−2222−222200-22-2200000000000−222200000000002−22−22−22−200000000000000000000000
χ874-4-4-4-4444-200002222-2-2-20000-4422−2222−22002-22-200000000000−22220000000000−22−222−22−200000000000000000000000
χ884-4-4-4-4444-200002222-2-2-20000-44−2222−2222002-22-20000000000022−2200000000002−22−2−22−2200000000000000000000000
χ8988-88-8-88-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-888-8-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000

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