Finite Group Databasebeta

← Group #10855258

Character table — Group #10855258

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666222244888812121212121212124444444446666881212121212122424242424242424444488884121212122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-11111-1-1-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1111-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-1-1-111111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111111-1-111111-1-1-1-1-1
χ911111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-11111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111111-1-1-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111-1-1111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1111111-1-1-111-1-11-1-111-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-22222-20000000000-2-2000000000000-2-22200000000000-20000000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-2-20000000000-2-200000000000022-2-20000000000020000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222222000000000022000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-22000000000022000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000022222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-2-222-1-1-1-1-2-2111111-1-1-1-1111100000000-211-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-2-1-1-1-1221111111111-1-1-1-1000000002-1-1110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-100002-2-2-2-2111122-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100002-2-2221111-2-2-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-222-2-21111-2-211-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-2222211112211-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ29222-2-22-2-22-22-222-2-22-22-222-2-2002i2i−2i−2i2-200002-200000002i−2i22-2-2000000002i2i−2i−2i0000000000000002i−2i0000000000
χ30222-2-22-2-22-22-222-2-22-22-222-2-200−2i−2i2i2i2-200002-20000000−2i2i22-2-200000000−2i−2i2i2i000000000000000−2i2i0000000000
χ31222-2-22-2-22-22-222-2-22-22-2-2-222002i2i−2i−2i2-200002-20000000−2i2i-2-222000000002i2i−2i−2i000000000000000−2i2i0000000000
χ32222-2-22-2-22-22-222-2-22-22-2-2-22200−2i−2i2i2i2-200002-200000002i−2i-2-22200000000−2i−2i2i2i0000000000000002i−2i0000000000
χ33222-2-22-2-2-1-22-22-111-11-1122-2-2002i2i−2i−2i-1133−3−3-1100000002i−2i-1-111003−333−3−3−i−iii−i3−i3i3i3000000000−i3i3−ii0000000000
χ34222-2-22-2-2-1-22-22-111-11-1122-2-2002i2i−2i−2i-11−3−333-1100000002i−2i-1-11100−33−3−333−i−iiii3i3−i3−i3000000000i3−i3−ii0000000000
χ35222-2-22-2-2-1-22-22-111-11-1122-2-200−2i−2i2i2i-1133−3−3-110000000−2i2i-1-111003−333−3−3ii−i−ii3i3−i3−i3000000000i3−i3i−i0000000000
χ36222-2-22-2-2-1-22-22-111-11-1122-2-200−2i−2i2i2i-11−3−333-110000000−2i2i-1-11100−33−3−333ii−i−i−i3−i3i3i3000000000−i3i3i−i0000000000
χ37222-2-22-2-2-1-22-22-111-11-11-2-222002i2i−2i−2i-1133−3−3-110000000−2i2i11-1-1003−3−3−333−i−iii−i3−i3i3i3000000000i3−i3i−i0000000000
χ38222-2-22-2-2-1-22-22-111-11-11-2-222002i2i−2i−2i-11−3−333-110000000−2i2i11-1-100−3333−3−3−i−iiii3i3−i3−i3000000000−i3i3i−i0000000000
χ39222-2-22-2-2-1-22-22-111-11-11-2-22200−2i−2i2i2i-1133−3−3-1100000002i−2i11-1-1003−3−3−333ii−i−ii3i3−i3−i3000000000−i3i3−ii0000000000
χ40222-2-22-2-2-1-22-22-111-11-11-2-22200−2i−2i2i2i-11−3−333-1100000002i−2i11-1-100−3333−3−3ii−i−i−i3−i3i3i3000000000i3−i3−ii0000000000
χ412-22-22-22-220000-22-2-222-200002i−2i−i2i2−i2i2002i−2i2i−2i002i2i−2i−2i0000000002−2000000−i2i2−i2i22−22−2002-222−2−2000000000000−i2i20
χ422-22-22-22-220000-22-2-222-200002i−2i−i2i2−i2i2002i−2i2i−2i00−2i−2i2i2i0000000002−2000000−i2i2−i2i22−22−200-22−2−222000000000000i2−i20
χ432-22-22-22-220000-22-2-222-200002i−2ii2−i2i2−i2002i−2i2i−2i002i2i−2i−2i000000000−22000000i2−i2i2−i2−22−22002-2−2−222000000000000i2−i20
χ442-22-22-22-220000-22-2-222-200002i−2ii2−i2i2−i2002i−2i2i−2i00−2i−2i2i2i000000000−22000000i2−i2i2−i2−22−2200-2222−2−2000000000000−i2i20
χ452-22-22-22-220000-22-2-222-20000−2i2i−i2i2−i2i200−2i2i−2i2i002i2i−2i−2i000000000−22000000−i2i2−i2i2−22−2200-2222−2−2000000000000i2−i20
χ462-22-22-22-220000-22-2-222-20000−2i2i−i2i2−i2i200−2i2i−2i2i00−2i−2i2i2i000000000−22000000−i2i2−i2i2−22−22002-2−2−222000000000000−i2i20
χ472-22-22-22-220000-22-2-222-20000−2i2ii2−i2i2−i200−2i2i−2i2i002i2i−2i−2i0000000002−2000000i2−i2i2−i22−22−200-22−2−222000000000000−i2i20
χ482-22-22-22-220000-22-2-222-20000−2i2ii2−i2i2−i200−2i2i−2i2i00−2i−2i2i2i0000000002−2000000i2−i2i2−i22−22−2002-222−2−2000000000000i2−i20
χ492-2-22-222-222-2-22-2222-2-2-22-22-2000000220000-2-22i−2i2i−2i000002-22-200000000000000002i−2i00000000000000002i−2i000
χ502-2-22-222-222-2-22-2222-2-2-22-22-2000000220000-2-2−2i2i−2i2i000002-22-20000000000000000−2i2i0000000000000000−2i2i000
χ512-2-22-222-222-2-22-2222-2-2-2-22-22000000220000-2-22i−2i2i−2i00000-22-2200000000000000002i−2i0000000000000000−2i2i000
χ522-2-22-222-222-2-22-2222-2-2-2-22-22000000220000-2-2−2i2i−2i2i00000-22-220000000000000000−2i2i00000000000000002i−2i000
χ532-2-22-222-22-222-2-2222-2-2-20000000000-2-20000222i−2i2i−2i02i−2i00000000002i−2i2i−2i00000000−2i2i000000000000002-200000
χ542-2-22-222-22-222-2-2222-2-2-20000000000-2-20000222i−2i2i−2i0−2i2i0000000000−2i2i−2i2i00000000−2i2i00000000000000-2200000
χ552-2-22-222-22-222-2-2222-2-2-20000000000-2-2000022−2i2i−2i2i02i−2i00000000002i−2i2i−2i000000002i−2i00000000000000-2200000
χ562-2-22-222-22-222-2-2222-2-2-20000000000-2-2000022−2i2i−2i2i0−2i2i0000000000−2i2i−2i2i000000002i−2i000000000000002-200000
χ572-2-2-222-222-2-222-2-2-222-222-2-220000002-20000-220000000002-2-22000000000000000000002-22-2000002-200000000
χ582-2-2-222-222-2-222-2-2-222-222-2-220000002-20000-220000000002-2-2200000000000000000000-22-2200000-2200000000
χ592-2-2-222-222-2-222-2-2-222-22-222-20000002-20000-22000000000-222-2000000000000000000002-22-200000-2200000000
χ602-2-2-222-222-2-222-2-2-222-22-222-20000002-20000-22000000000-222-200000000000000000000-22-22000002-200000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-2220000-400000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000040000000000-2-200000000000000000000000000000000000
χ63444-4-44-4-444-44-44-4-44-44-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ64444-4-44-4-4-24-44-4-222-22-2200000000002-22323−23−232-2000000000000000−232300000000000000000000000000000000000
χ65444-4-44-4-4-24-44-4-222-22-2200000000002-2−23−2323232-200000000000000023−2300000000000000000000000000000000000
χ6644-444-4-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ6744-444-4-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ6844-4-4-4-4444000044-4-4-4-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ6944-4-4-4-4444000044-4-4-4-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ704-444-4-4-4440000-4-44-4-44400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ714-444-4-4-4440000-4-44-4-444000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ724-444-4-4-44-2000022-222-2-200000022−22−222200−2i32i32i3−2i300000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ734-444-4-4-44-2000022-222-2-200000022−22−2222002i3−2i3−2i32i300000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ744-444-4-4-44-2000022-222-2-2000000−222222−2200−2i32i32i3−2i3000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ754-444-4-4-44-2000022-222-2-2000000−222222−22002i3−2i3−2i32i3000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ764-44-44-44-4-200002-222-2-2200004i−4i−2i22i2−2i22i200−2i2i−2i2i00000000000000022−22000000i2−i2i2−i2−22−2200000000000000000000000
χ774-44-44-44-4-200002-222-2-2200004i−4i2i2−2i22i2−2i200−2i2i−2i2i000000000000000−2222000000−i2i2−i2i22−22−200000000000000000000000
χ784-44-44-44-4-200002-222-2-220000−4i4i−2i22i2−2i22i2002i−2i2i−2i000000000000000−2222000000i2−i2i2−i22−22−200000000000000000000000
χ794-44-44-44-4-200002-222-2-220000−4i4i2i2−2i22i2−2i2002i−2i2i−2i00000000000000022−22000000−i2i2−i2i2−22−2200000000000000000000000
χ804-4-44-444-4-24-4-442-2-2-22224-44-4000000-2-2000022000000000-22-22000000000000000000000000000000000000000
χ814-4-44-444-4-24-4-442-2-2-2222-44-44000000-2-20000220000000002-22-2000000000000000000000000000000000000000
χ824-4-44-444-4-2-444-42-2-2-22220000000000220000-2-2000004i−4i0000000000−2i2i−2i2i0000000000000000000000000000000
χ834-4-44-444-4-2-444-42-2-2-22220000000000220000-2-200000−4i4i00000000002i−2i2i−2i0000000000000000000000000000000
χ844-4-4-444-44444-4-4-4-4-444-440000000000-4400004-40000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-244-4-4222-2-22-200000000002-20000-2200000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ864-4-4-444-44-244-4-4222-2-22-200000000002-20000-22000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ874-4-4-444-44-2-4-444222-2-22-24-4-44000000-2200002-2000000000-222-2000000000000000000000000000000000000000
χ884-4-4-444-44-2-4-444222-2-22-2-444-4000000-2200002-20000000002-2-22000000000000000000000000000000000000000
χ8988-888-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-8-888-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000

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