Finite Group Databasebeta

← Group #72271699

Character table — Group #72271699

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222222222444444444488888888888888888812121212161616161616161616161616161616161616161616161616162424242424242424323232323248484848484848484896
order12222344446666688881212121244444412121212161616162424242422442224666681212121216162424484848484848484824881616161668122424244444816168
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111-1-1111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111
χ5111111111111111111111111111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111111-11-1-11111-1-1-1-1-1-1
χ6111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-11-1-1-1-1-1-1111111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-11-111-1-111-1-1-1111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-11-11111-1-1111-1-1-1
χ911111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111-1
χ1011111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11
χ1111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-11-1-11
χ1211111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-111-1
χ1311111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-11-111-1-1-1-111-1-1-11
χ1411111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11-1111111-1-1111-1
χ1511111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11-11-1-111-1-111-111-1
χ1611111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1111111-1-111111-11-1-1-1-111-1-11-1-11
χ17222222222222222-2-2-2-2222200002222220000-2-2-2-2222200000000-2000000-2-20000000022-2-2000000000000000-2000
χ18222222222222222-2-2-2-2222200002222220000-2-2-2-2-2-2-2-200000000-2000000-2-200000000-2-2220000000000000002000
χ19222222222222222-2-2-2-222220000-2-2-2-2-2-20000-2-2-2-222220000000020000002200000000-2-2-2-20000000000000002000
χ20222222222222222-2-2-2-222220000-2-2-2-2-2-20000-2-2-2-2-2-2-2-200000000200000022000000002222000000000000000-2000
χ2122222-12222-1-1-1-1-12222-1-1-1-1222222-1-1-1-12222-1-1-1-100002222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-12-1-1-10000000000
χ2222222-12222-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-1000022-2-2-1-1-1-12-1-1-1-1-2-2-1-111111111000000001-21110000000000
χ2322222-12222-1-1-1-1-12222-1-1-1-12222-2-211112222-1-1-1-10000-2-2221111-2-1-1-1-1-2-211-1-1-1-1111100000000-1-2-1110000000000
χ2422222-12222-1-1-1-1-12222-1-1-1-12222-2-21111-2-2-2-2-1-1-1-10000-2-2-2-21111-2-1-1-1-122111111-1-1-1-100000000121-1-10000000000
χ2522222-12222-1-1-1-1-12222-1-1-1-1-2-2-2-222-1-1-1-12222-1-1-1-10000-2-2-2-211112111122-1-1-1-1-1-1-1-1-1-1000000001-21110000000000
χ2622222-12222-1-1-1-1-12222-1-1-1-1-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-10000-2-222111121111-2-2-1-11111111100000000-12-1-1-10000000000
χ2722222-12222-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-211112222-1-1-1-1000022-2-2-1-1-1-1-21111-2-211-1-1-1-1111100000000121-1-10000000000
χ2822222-12222-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-21111-2-2-2-2-1-1-1-100002222-1-1-1-1-2111122111111-1-1-1-100000000-1-2-1110000000000
χ29222-2-22-22-22-2-222-22-22-2-22-222i2i−2i−2i000000000022-2-200000000000002i2i−2i−2i00000000000000002i2i−2i−2i000002-200000000
χ30222-2-22-22-22-2-222-22-22-2-22-222i2i−2i−2i000000000022-2-200000000000002i2i−2i−2i0000000000000000−2i−2i2i2i00000-2200000000
χ31222-2-22-22-22-2-222-22-22-2-22-22−2i−2i2i2i000000000022-2-20000000000000−2i−2i2i2i00000000000000002i2i−2i−2i00000-2200000000
χ32222-2-22-22-22-2-222-22-22-2-22-22−2i−2i2i2i000000000022-2-20000000000000−2i−2i2i2i0000000000000000−2i−2i2i2i000002-200000000
χ3322-22-22-2-222222-2-222-2-222-2-22i−2i2i−2i0000002i2i−2i−2i2-22-20000002-2000002i−2i2i−2i00002i2i−2i−2i00000000000020-2000000000000
χ3422-22-22-2-222222-2-222-2-222-2-22i−2i2i−2i000000−2i−2i2i2i2-22-2000000-22000002i−2i2i−2i0000−2i−2i2i2i000000000000-202000000000000
χ3522-22-22-2-222222-2-222-2-222-2-2−2i2i−2i2i0000002i2i−2i−2i2-22-2000000-2200000−2i2i−2i2i00002i2i−2i−2i000000000000-202000000000000
χ3622-22-22-2-222222-2-222-2-222-2-2−2i2i−2i2i000000−2i−2i2i2i2-22-20000002-200000−2i2i−2i2i0000−2i−2i2i2i00000000000020-2000000000000
χ3722-22-2-1-2-222-1-1-11122-2-2-1-1112i−2i2i−2i0033−3−32i2i−2i−2i-11-110000002-2−i3−i3i3i30−ii−ii003−3−i−iii−i3−i3i3i300000000-1013−30000000000
χ3822-22-2-1-2-222-1-1-11122-2-2-1-1112i−2i2i−2i0033−3−3−2i−2i2i2i-11-11000000-22−i3−i3i3i30−ii−ii003−3ii−i−ii3i3−i3−i30000000010-1−330000000000
χ3922-22-2-1-2-222-1-1-11122-2-2-1-1112i−2i2i−2i00−3−3332i2i−2i−2i-11-110000002-2i3i3−i3−i30−ii−ii00−33−i−iiii3i3−i3−i300000000-101−330000000000
χ4022-22-2-1-2-222-1-1-11122-2-2-1-1112i−2i2i−2i00−3−333−2i−2i2i2i-11-11000000-22i3i3−i3−i30−ii−ii00−33ii−i−i−i3−i3i3i30000000010-13−30000000000
χ4122-22-2-1-2-222-1-1-11122-2-2-1-111−2i2i−2i2i0033−3−32i2i−2i−2i-11-11000000-22i3i3−i3−i30i−ii−i003−3−i−iii−i3−i3i3i30000000010-1−330000000000
χ4222-22-2-1-2-222-1-1-11122-2-2-1-111−2i2i−2i2i0033−3−3−2i−2i2i2i-11-110000002-2i3i3−i3−i30i−ii−i003−3ii−i−ii3i3−i3−i300000000-1013−30000000000
χ4322-22-2-1-2-222-1-1-11122-2-2-1-111−2i2i−2i2i00−3−3332i2i−2i−2i-11-11000000-22−i3−i3i3i30i−ii−i00−33−i−iiii3i3−i3−i30000000010-13−30000000000
χ4422-22-2-1-2-222-1-1-11122-2-2-1-111−2i2i−2i2i00−3−333−2i−2i2i2i-11-110000002-2−i3−i3i3i30i−ii−i00−33ii−i−i−i3−i3i3i300000000-101−330000000000
χ4522-2-2222-2-22-2-22-222-2-22-222-22-2-2200000000002-2-222-22-20000000002-2-22000000000000002-2000000000002-2000000
χ4622-2-2222-2-22-2-22-222-2-22-222-22-2-2200000000002-2-22-22-220000000002-2-2200000000000000-2200000000000-22000000
χ4722-2-2222-2-22-2-22-222-2-22-222-2-222-200000000002-2-222-22-2000000000-222-2000000000000002-200000000000-22000000
χ4822-2-2222-2-22-2-22-222-2-22-222-2-222-200000000002-2-22-22-22000000000-222-200000000000000-22000000000002-2000000
χ4922-2-2222-2-22-2-22-22-222-2-222-200000000000000-222-22-22-22-2002-22-20000000000000000000-2200000000000002-20000
χ5022-2-2222-2-22-2-22-22-222-2-222-200000000000000-222-22-22-2-2200-22-220000000000000000000-220000000000000-220000
χ5122-2-2222-2-22-2-22-22-222-2-222-200000000000000-222-2-22-222-2002-22-200000000000000000002-20000000000000-220000
χ5222-2-2222-2-22-2-22-22-222-2-222-200000000000000-222-2-22-22-2200-22-2200000000000000000002-200000000000002-20000
χ5322-2-222-222-2-2-22-2200002-2-2200002-22-22-22−22−2000022-2-200000000000002−2002−22−22−22−22-2002−22−20000000000002−20
χ5422-2-222-222-2-2-22-2200002-2-2200002-22-22-22−22−20000-2-22200000000000002−2002−22−22−22−2-2200−22−22000000000000−220
χ5522-2-222-222-2-2-22-2200002-2-2200002-22-22-2−22−22000022-2-20000000000000−2200−22−22−22−222-200−22−22000000000000−220
χ5622-2-222-222-2-2-22-2200002-2-2200002-22-22-2−22−220000-2-2220000000000000−2200−22−22−22−22-22002−22−20000000000002−20
χ5722-2-222-222-2-2-22-2200002-2-220000-22-22-222−22−2000022-2-20000000000000−22002−22−2−22−22-22002−22−2000000000000−220
χ5822-2-222-222-2-2-22-2200002-2-220000-22-22-222−22−20000-2-2220000000000000−22002−22−2−22−222-200−22−220000000000002−20
χ5922-2-222-222-2-2-22-2200002-2-220000-22-22-22−22−22000022-2-200000000000002−200−22−222−22−2-2200−22−220000000000002−20
χ6022-2-222-222-2-2-22-2200002-2-220000-22-22-22−22−220000-2-22200000000000002−200−22−222−22−22-2002−22−2000000000000−220
χ61444444-4-4-4-4444440000-4-4-4-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ62444444-4-4-4-4444440000-4-4-4-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ6344444-24444-2-2-2-2-2-4-4-4-4-2-2-2-2000044-2-2-2-200002222000000000000-4000000220000000000000000000000000000000
χ6444444-24444-2-2-2-2-2-4-4-4-4-2-2-2-20000-4-42222000022220000000000004000000-2-20000000000000000000000000000000
χ65444-4-444-44-4-4-444-400004-44-40000000000−2i22i22i2−2i20000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ66444-4-444-44-4-4-444-400004-44-400000000002i2−2i2−2i22i200000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ67444-4-44-44-44-4-444-4-44-44-44-4400000000000000-4-4440000000000000000000000000000000000000000000000000000
χ68444-4-4-24-44-422-2-220000-22-2200000023−23−2323−2i22i22i2−2i20000000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000
χ69444-4-4-24-44-422-2-220000-22-2200000023−23−23232i2−2i2−2i22i20000000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000
χ70444-4-4-24-44-422-2-220000-22-22000000−232323−23−2i22i22i2−2i20000000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000
χ71444-4-4-24-44-422-2-220000-22-22000000−232323−232i2−2i2−2i22i20000000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000
χ72444-4-4-2-44-4422-2-224-44-42-22-24i4i−4i−4i0000000000-2-2220000000000000−2i−2i2i2i00000000000000000000000000000000000
χ73444-4-4-2-44-4422-2-224-44-42-22-2−4i−4i4i4i0000000000-2-22200000000000002i2i−2i−2i00000000000000000000000000000000000
χ74444-4-4-2-44-4422-2-22-44-442-22-20000000000000022-2-200000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ75444-4-4-2-44-4422-2-22-44-442-22-20000000000000022-2-2000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ7644-44-4444-4-4444-4-40000-4-444000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ7744-44-4444-4-4444-4-40000-4-4440000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ7844-44-44-4-444444-4-4-4-44444-4-400000000000000-44-440000000000000000000000000000000000000000000000000000
χ7944-44-4-2-4-444-2-2-222-4-444-2-2220000002323−23−2300002-22-20000000000000000000−23230000000000000000000000000000000
χ8044-44-4-2-4-444-2-2-222-4-444-2-222000000−23−23232300002-22-2000000000000000000023−230000000000000000000000000000000
χ8144-4-44-24-4-4422-22-24-4-442-2-224-4-440000000000-222-20000000000000-222-200000000000000000000000000000000000
χ8244-4-44-24-4-4422-22-24-4-442-2-22-444-40000000000-222-200000000000002-2-2200000000000000000000000000000000000
χ8344-4-44-24-4-4422-22-2-444-42-2-22000000000000002-2-2200004-400-22-220000000000000000000000000000000000000000
χ8444-4-44-24-4-4422-22-2-444-42-2-22000000000000002-2-220000-44002-22-20000000000000000000000000000000000000000
χ8544-4-44-2-444-422-22-20000-222-200004-4-22-2222−2222−2200000000000000000000022−2200−22−22−22−2200000000000000000000000
χ8644-4-44-2-444-422-22-20000-222-200004-4-22-22−2222−2222000000000000000000000−2222002−22−22−22−200000000000000000000000
χ8744-4-44-2-444-422-22-20000-222-20000-442-22-222−2222−22000000000000000000000−222200−22−222−22−200000000000000000000000
χ8844-4-44-2-444-422-22-20000-222-20000-442-22-2−2222−222200000000000000000000022−22002−22−2−22−2200000000000000000000000
χ8988888-4-8-8-8-8-4-4-4-4-4000044440000000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-8-488-8-8-4-4-444000044-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ9116-1600016000000-1600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9216-16000-80000−8i38i3800000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9316-16000-800008i3−8i3800000000000000000000000000000000000000000000000000000000000000000000000000000000

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