Finite Group Databasebeta

← Group #10829921

Character table — Group #10829921

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244442222466668812121212121224242424242424244444888846612122222444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111-1-111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-111-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-111-1-111-1-1-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1111-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-11111-1-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111111-1-111-1-111111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111-1-111-1-111-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-11111-1-111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-111-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-111-1-111-1-11-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-222220000-2000000-2-2000000000000-2-2220000000000000-200000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-20000-2000000-2-200000000000022-2-20000000000000200000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220000200000022000000000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-2000020000002200000000000022220000000000000-200000
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
χ29222-22-2-2-22-2-22222-22-2-2-22i2i−2i−2i002i2i−2i−2i2-200002-20000002-20000000002i2i−2i−2i2i2i−2i−2i00000000000002-2000000000000
χ30222-22-2-2-22-2-22222-22-2-2-22i2i−2i−2i00−2i−2i2i2i2-200002-2000000-220000000002i2i−2i−2i−2i−2i2i2i0000000000000-22000000000000
χ31222-22-2-2-22-2-22222-22-2-2-2−2i−2i2i2i002i2i−2i−2i2-200002-2000000-22000000000−2i−2i2i2i2i2i−2i−2i0000000000000-22000000000000
χ32222-22-2-2-22-2-22222-22-2-2-2−2i−2i2i2i00−2i−2i2i2i2-200002-20000002-2000000000−2i−2i2i2i−2i−2i2i2i00000000000002-2000000000000
χ33222-22-2-2-2-1-2-222-1-11-11112i2i−2i−2i002i2i−2i−2i-1133−3−3-110000002-20−i3−i3i3i3003−3−i−iii−i−iii−i3−i3i3i3000000000-113−30000000000
χ34222-22-2-2-2-1-2-222-1-11-11112i2i−2i−2i002i2i−2i−2i-11−3−333-110000002-20i3i3−i3−i300−33−i−iii−i−iiii3i3−i3−i3000000000-11−330000000000
χ35222-22-2-2-2-1-2-222-1-11-11112i2i−2i−2i00−2i−2i2i2i-1133−3−3-11000000-220−i3−i3i3i3003−3−i−iiiii−i−ii3i3−i3−i30000000001-1−330000000000
χ36222-22-2-2-2-1-2-222-1-11-11112i2i−2i−2i00−2i−2i2i2i-11−3−333-11000000-220i3i3−i3−i300−33−i−iiiii−i−i−i3−i3i3i30000000001-13−30000000000
χ37222-22-2-2-2-1-2-222-1-11-1111−2i−2i2i2i002i2i−2i−2i-1133−3−3-11000000-220i3i3−i3−i3003−3ii−i−i−i−iii−i3−i3i3i30000000001-1−330000000000
χ38222-22-2-2-2-1-2-222-1-11-1111−2i−2i2i2i002i2i−2i−2i-11−3−333-11000000-220−i3−i3i3i300−33ii−i−i−i−iiii3i3−i3−i30000000001-13−30000000000
χ39222-22-2-2-2-1-2-222-1-11-1111−2i−2i2i2i00−2i−2i2i2i-1133−3−3-110000002-20i3i3−i3−i3003−3ii−i−iii−i−ii3i3−i3−i3000000000-113−30000000000
χ40222-22-2-2-2-1-2-222-1-11-1111−2i−2i2i2i00−2i−2i2i2i-11−3−333-110000002-20−i3−i3i3i300−33ii−i−iii−i−i−i3−i3i3i3000000000-11−330000000000
χ4122-2-2-2-222200002-2-2-2-22200002-22−22−2002-22-20022-2-20000000002−20000002−22−22−22−2002-222−2−20000000000002−20
χ4222-2-2-2-222200002-2-2-2-22200002-22−22−2002-22-200-2-2220000000002−20000002−22−22−22−200-22−2−222000000000000−220
χ4322-2-2-2-222200002-2-2-2-22200002-2−22−22002-22-20022-2-2000000000−22000000−22−22−22−22002-2−2−222000000000000−220
χ4422-2-2-2-222200002-2-2-2-22200002-2−22−22002-22-200-2-222000000000−22000000−22−22−22−2200-2222−2−20000000000002−20
χ4522-2-2-2-222200002-2-2-2-2220000-222−22−200-22-220022-2-2000000000−220000002−22−2−22−2200-2222−2−2000000000000−220
χ4622-2-2-2-222200002-2-2-2-2220000-222−22−200-22-2200-2-222000000000−220000002−22−2−22−22002-2−2−2220000000000002−20
χ4722-2-2-2-222200002-2-2-2-2220000-22−22−2200-22-220022-2-20000000002−2000000−22−222−22−200-22−2−2220000000000002−20
χ4822-2-2-2-222200002-2-2-2-2220000-22−22−2200-22-2200-2-2220000000002−2000000−22−222−22−2002-222−2−2000000000000−220
χ492-2-222-22-222-22-2-2-222-22-22i−2i2i−2i000000220000-2-2000000000000000002i−2i2i−2i0000000000002-22-200000000002i−2i000
χ502-2-222-22-222-22-2-2-222-22-22i−2i2i−2i000000220000-2-2000000000000000002i−2i2i−2i000000000000-22-220000000000−2i2i000
χ512-2-222-22-222-22-2-2-222-22-2−2i2i−2i2i000000220000-2-200000000000000000−2i2i−2i2i0000000000002-22-20000000000−2i2i000
χ522-2-222-22-222-22-2-2-222-22-2−2i2i−2i2i000000220000-2-200000000000000000−2i2i−2i2i000000000000-22-2200000000002i−2i000
χ532-2-2-222-2222-2-22-2-2-222-220000000000-2200002-22-22-22-20002-22-200000000000000002-200000000000002-2000000
χ542-2-2-222-2222-2-22-2-2-222-220000000000-2200002-22-22-2-22000-22-2200000000000000002-20000000000000-22000000
χ552-2-2-222-2222-2-22-2-2-222-220000000000-2200002-2-22-222-20002-22-20000000000000000-220000000000000-22000000
χ562-2-2-222-2222-2-22-2-2-222-220000000000-2200002-2-22-22-22000-22-220000000000000000-2200000000000002-2000000
χ572-2-2-222-222-222-2-2-2-222-222-2-220000002-20000-222-22-200000000000002-2-2200000000-22000000000002-200000000
χ582-2-2-222-222-222-2-2-2-222-222-2-220000002-20000-22-22-2200000000000002-2-22000000002-200000000000-2200000000
χ592-2-2-222-222-222-2-2-2-222-22-222-20000002-20000-222-22-20000000000000-222-200000000-2200000000000-2200000000
χ602-2-2-222-222-222-2-2-2-222-22-222-20000002-20000-22-22-220000000000000-222-2000000002-2000000000002-200000000
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
χ63444-44-4-4-4444-4-444-44-4-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-244-4-4-2-22-222200000000002-22323−23−232-2000000000000000−232300000000000000000000000000000000000
χ65444-44-4-4-4-244-4-4-2-22-222200000000002-2−23−2323232-200000000000000023−2300000000000000000000000000000000000
χ6644-44-44-4-4400004-44-44-4-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ6744-44-44-4-4400004-44-44-4-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ6844-44-44-4-4-20000-22-22-222000000−2i22i22i2−2i20023−23−232300000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000
χ6944-44-44-4-4-20000-22-22-222000000−2i22i22i2−2i200−232323−2300000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000
χ7044-44-44-4-4-20000-22-22-2220000002i2−2i2−2i22i20023−23−232300000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000
χ7144-44-44-4-4-20000-22-22-2220000002i2−2i2−2i22i200−232323−2300000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000
χ7244-4-4-4-444-20000-22222-2-200004-422−2222−2200-22-2200000000000000022−22000000−22−22−22−2200000000000000000000000
χ7344-4-4-4-444-20000-22222-2-200004-4−2222−222200-22-22000000000000000−22220000002−22−22−22−200000000000000000000000
χ7444-4-4-4-444-20000-22222-2-20000-4422−2222−22002-22-2000000000000000−2222000000−22−222−22−200000000000000000000000
χ7544-4-4-4-444-20000-22222-2-20000-44−2222−2222002-22-200000000000000022−220000002−22−2−22−2200000000000000000000000
χ764-444-4-4-4440000-444-4-4-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ774-444-4-4-4440000-444-4-4-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ784-44-4-444-440000-44-4-444-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ794-44-4-444-440000-44-4-444-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ804-4-444-44-44-44-44-4-444-44-40000000000-4-40000440000000000000000000000000000000000000000000000000000
χ814-4-444-44-4-24-44-422-2-22-224i−4i4i−4i000000-2-200002200000000000000000−2i2i−2i2i0000000000000000000000000000000
χ824-4-444-44-4-24-44-422-2-22-22−4i4i−4i4i000000-2-2000022000000000000000002i−2i2i−2i0000000000000000000000000000000
χ834-4-444-44-4-2-44-4422-2-22-220000000000220000-2-2000000000−2i32i32i3−2i3000000000000000000000000000000000000000
χ844-4-444-44-4-2-44-4422-2-22-220000000000220000-2-20000000002i3−2i3−2i32i3000000000000000000000000000000000000000
χ854-4-4-444-44-24-4-44222-2-22-200000000002-20000-2200004-4000-22-22000000000000000000000000000000000000000
χ864-4-4-444-44-24-4-44222-2-22-200000000002-20000-220000-440002-22-2000000000000000000000000000000000000000
χ874-4-4-444-44-2-444-4222-2-22-24-4-44000000-2200002-200000000000000000-222-20000000000000000000000000000000
χ884-4-4-444-44-2-444-4222-2-22-2-444-4000000-2200002-2000000000000000002-2-220000000000000000000000000000000
χ898-888-8-8-88-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-888-8-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000000000

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