Finite Group Databasebeta

← Group #10827373

Character table — Group #10827373

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121222222222466668812121212121224242424242424244444888846612122224444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111-1-111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-111-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-111-1-1-111-1-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-111-1-11-1-111-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-111111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111111-1-11111111-1-1-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111-1-111-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-111111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-11111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-111-1-11-1-1-1-111-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-222220000-2000000-2-2000000000000-2-222000000000-2000000000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-20000-2000000-2-200000000000022-2-20000000002000000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220000200000022000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-200002000000220000000000002222000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1000022-2-22-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-222-21111-2-211-1-1-1-1-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-211112211-1-1-1-11111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-2-2-22111122-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000-2-22221111-2-2-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-1000022-2-2-2-1-1-1-1-2-2111111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-100002222-2-1-1-1-1221111111111-1-1-1-100000000-2-1-1110000000000
χ29222-2-22-2-22000022-22-2-2-200002i−2i−i2−i2i2i2002i2i−2i−2i0022-2-20000000002−2000000−i2−i2i2i222−2−2002i−2i−i2−i2i2i20000000000002−20
χ30222-2-22-2-22000022-22-2-2-200002i−2i−i2−i2i2i2002i2i−2i−2i00-2-2220000000002−2000000−i2−i2i2i222−2−200−2i2ii2i2−i2−i2000000000000−220
χ31222-2-22-2-22000022-22-2-2-200002i−2ii2i2−i2−i2002i2i−2i−2i0022-2-2000000000−22000000i2i2−i2−i2−2−222002i−2ii2i2−i2−i2000000000000−220
χ32222-2-22-2-22000022-22-2-2-200002i−2ii2i2−i2−i2002i2i−2i−2i00-2-222000000000−22000000i2i2−i2−i2−2−22200−2i2i−i2−i2i2i20000000000002−20
χ33222-2-22-2-22000022-22-2-2-20000−2i2i−i2−i2i2i200−2i−2i2i2i0022-2-2000000000−22000000−i2−i2i2i2−2−22200−2i2i−i2−i2i2i2000000000000−220
χ34222-2-22-2-22000022-22-2-2-20000−2i2i−i2−i2i2i200−2i−2i2i2i00-2-222000000000−22000000−i2−i2i2i2−2−222002i−2ii2i2−i2−i20000000000002−20
χ35222-2-22-2-22000022-22-2-2-20000−2i2ii2i2−i2−i200−2i−2i2i2i0022-2-20000000002−2000000i2i2−i2−i222−2−200−2i2ii2i2−i2−i20000000000002−20
χ36222-2-22-2-22000022-22-2-2-20000−2i2ii2i2−i2−i200−2i−2i2i2i00-2-2220000000002−2000000i2i2−i2−i222−2−2002i−2i−i2−i2i2i2000000000000−220
χ3722-22-2-22-222-22-22-2-2-222-22i2i−2i−2i000000220000-2-2000000000000000002i2i−2i−2i0000000000002i−2i2i−2i0000002-20000000
χ3822-22-2-22-222-22-22-2-2-222-22i2i−2i−2i000000220000-2-2000000000000000002i2i−2i−2i000000000000−2i2i−2i2i000000-220000000
χ3922-22-2-22-222-22-22-2-2-222-2−2i−2i2i2i000000220000-2-200000000000000000−2i−2i2i2i0000000000002i−2i2i−2i000000-220000000
χ4022-22-2-22-222-22-22-2-2-222-2−2i−2i2i2i000000220000-2-200000000000000000−2i−2i2i2i000000000000−2i2i−2i2i0000002-20000000
χ412-22-22-22-2222-2-2-222-22-2-22i−2i2i−2i002i−2i2i−2i2-200002-20000002-20000000002i−2i2i−2i2i−2i2i−2i00000000000002-2000000000000
χ422-22-22-22-2222-2-2-222-22-2-22i−2i2i−2i00−2i2i−2i2i2-200002-2000000-220000000002i−2i2i−2i−2i2i−2i2i0000000000000-22000000000000
χ432-22-22-22-2222-2-2-222-22-2-2−2i2i−2i2i002i−2i2i−2i2-200002-2000000-22000000000−2i2i−2i2i2i−2i2i−2i0000000000000-22000000000000
χ442-22-22-22-2222-2-2-222-22-2-2−2i2i−2i2i00−2i2i−2i2i2-200002-20000002-2000000000−2i2i−2i2i−2i2i−2i2i00000000000002-2000000000000
χ452-22-22-22-2-122-2-21-1-11-1112i−2i2i−2i002i−2i2i−2i-113−33−3-110000002-20−i3−i3i3i3003−3−ii−ii−ii−ii−i3i3−i3i3000000000-113−30000000000
χ462-22-22-22-2-122-2-21-1-11-1112i−2i2i−2i002i−2i2i−2i-11−33−33-110000002-20i3i3−i3−i300−33−ii−ii−ii−iii3−i3i3−i3000000000-11−330000000000
χ472-22-22-22-2-122-2-21-1-11-1112i−2i2i−2i00−2i2i−2i2i-113−33−3-11000000-220−i3−i3i3i3003−3−ii−iii−ii−ii3−i3i3−i30000000001-1−330000000000
χ482-22-22-22-2-122-2-21-1-11-1112i−2i2i−2i00−2i2i−2i2i-11−33−33-11000000-220i3i3−i3−i300−33−ii−iii−ii−i−i3i3−i3i30000000001-13−30000000000
χ492-22-22-22-2-122-2-21-1-11-111−2i2i−2i2i002i−2i2i−2i-113−33−3-11000000-220i3i3−i3−i3003−3i−ii−i−ii−ii−i3i3−i3i30000000001-1−330000000000
χ502-22-22-22-2-122-2-21-1-11-111−2i2i−2i2i002i−2i2i−2i-11−33−33-11000000-220−i3−i3i3i300−33i−ii−i−ii−iii3−i3i3−i30000000001-13−30000000000
χ512-22-22-22-2-122-2-21-1-11-111−2i2i−2i2i00−2i2i−2i2i-113−33−3-110000002-20i3i3−i3−i3003−3i−ii−ii−ii−ii3−i3i3−i3000000000-113−30000000000
χ522-22-22-22-2-122-2-21-1-11-111−2i2i−2i2i00−2i2i−2i2i-11−33−33-110000002-20−i3−i3i3i300−33i−ii−ii−ii−i−i3i3−i3i3000000000-11−330000000000
χ532-2-2-2-222222-2-22-2-2-222-222-2-220000002-20000-222-22-200000000000002-2-22000000002-200000000000000002-2000
χ542-2-2-2-222222-2-22-2-2-222-222-2-220000002-20000-22-22-2200000000000002-2-2200000000-220000000000000000-22000
χ552-2-2-2-222222-2-22-2-2-222-22-222-20000002-20000-222-22-20000000000000-222-2000000002-20000000000000000-22000
χ562-2-2-2-222222-2-22-2-2-222-22-222-20000002-20000-22-22-220000000000000-222-200000000-2200000000000000002-2000
χ572-2-2-2-22222-222-2-2-2-222-220000000000-2200002-22-22-22-20002-22-20000000000000000-22000000000000002-200000
χ582-2-2-2-22222-222-2-2-2-222-220000000000-2200002-22-22-2-22000-22-220000000000000000-2200000000000000-2200000
χ592-2-2-2-22222-222-2-2-2-222-220000000000-2200002-2-22-222-20002-22-200000000000000002-200000000000000-2200000
χ602-2-2-2-22222-222-2-2-2-222-220000000000-2200002-2-22-22-22000-22-2200000000000000002-2000000000000002-200000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-22200000000-40000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000000004000000-2-200000000000000000000000000000000000
χ63444-4-44-4-4-20000-2-22-222200004i−4i−2i2−2i22i22i200−2i−2i2i2i00000000000000022−22000000i2i2−i2−i2−2−22200000000000000000000000
χ64444-4-44-4-4-20000-2-22-222200004i−4i2i22i2−2i2−2i200−2i−2i2i2i000000000000000−2222000000−i2−i2i2i222−2−200000000000000000000000
χ65444-4-44-4-4-20000-2-22-22220000−4i4i−2i2−2i22i22i2002i2i−2i−2i000000000000000−2222000000i2i2−i2−i222−2−200000000000000000000000
χ66444-4-44-4-4-20000-2-22-22220000−4i4i2i22i2−2i2−2i2002i2i−2i−2i00000000000000022−22000000−i2−i2i2i2−2−22200000000000000000000000
χ6744-44-4-44-44-44-444-4-4-444-40000000000-4-40000440000000000000000000000000000000000000000000000000000
χ6844-44-4-44-4-24-44-4-2222-2-224i4i−4i−4i000000-2-200002200000000000000000−2i−2i2i2i0000000000000000000000000000000
χ6944-44-4-44-4-24-44-4-2222-2-22−4i−4i4i4i000000-2-2000022000000000000000002i2i−2i−2i0000000000000000000000000000000
χ7044-44-4-44-4-2-44-44-2222-2-220000000000220000-2-2000000000−2i32i32i3−2i3000000000000000000000000000000000000000
χ7144-44-4-44-4-2-44-44-2222-2-220000000000220000-2-20000000002i3−2i3−2i32i3000000000000000000000000000000000000000
χ7244-4-44-4-44400004-44-4-4-4400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ7344-4-44-4-44400004-44-4-4-44000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ744-444-4-4-4440000-44-4-4-44400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ754-444-4-4-4440000-44-4-4-444000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ764-444-4-4-44-200002-2222-2-200000022−22−222200−2i32i32i3−2i300000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ774-444-4-4-44-200002-2222-2-200000022−22−2222002i3−2i3−2i32i300000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ784-444-4-4-44-200002-2222-2-2000000−222222−2200−2i32i32i3−2i3000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ794-444-4-4-44-200002-2222-2-2000000−222222−22002i3−2i3−2i32i3000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ804-44-44-44-44-4-444-444-44-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ814-44-44-44-4-2-4-4442-2-22-22200000000002-223−2323−232-2000000000000000−232300000000000000000000000000000000000
χ824-44-44-44-4-2-4-4442-2-22-22200000000002-2−2323−23232-200000000000000023−2300000000000000000000000000000000000
χ834-4-4444-4-440000-4-444-44-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ844-4-4444-4-440000-4-444-44-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-24-4-44222-2-22-24-4-44000000-2200002-200000000000000000-222-20000000000000000000000000000000
χ864-4-4-4-4444-24-4-44222-2-22-2-444-4000000-2200002-2000000000000000002-2-220000000000000000000000000000000
χ874-4-4-4-4444-2-444-4222-2-22-200000000002-20000-2200004-4000-22-22000000000000000000000000000000000000000
χ884-4-4-4-4444-2-444-4222-2-22-200000000002-20000-220000-440002-22-2000000000000000000000000000000000000000
χ8988-8-88-8-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8888-8-8-4000044-4-44-440000000000000000000000000000000000000000000000000000000000000000000000

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