Finite Group Databasebeta

← Group #11723113

Character table — Group #11723113

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size112222244444444444444444444444444444444444444444444444444418183636363636108108108108
order12236662333333666666666666666666666666666666666666666666664426612128888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1ii−i−i
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1−i−iii
χ51111111-1111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-11-1
χ61111111-1111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11-11
χ71111111-1111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1i−i−ii
χ81111111-1111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1−iii−i
χ9222-1-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-10000
χ10222-1-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-211110000
χ11222-1-1-1-1-222-1-1-1-111222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111122-211-1-10000
χ12222-1-1-1-1-222-1-1-1-111222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-2-22-1-1110000
χ1322-22-2-2202222220022-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000002-20002-20000
χ1422-22-2-2202222220022-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000-22000-220000
χ1522-2-111-1022-1-1-1-1−i3i322-2-2-2-2-1-1-1-11111111100000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32-20−i3i3-110000
χ1622-2-111-1022-1-1-1-1−i3i322-2-2-2-2-1-1-1-11111111100000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-220i3−i31-10000
χ1722-2-111-1022-1-1-1-1i3−i322-2-2-2-2-1-1-1-11111111100000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32-20i3−i3-110000
χ1822-2-111-1022-1-1-1-1i3−i322-2-2-2-2-1-1-1-11111111100000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-220−i3i31-10000
χ19444444441-211-2-2441-211-2-211-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-200000000000
χ2044444444-21-2-21144-21-2-211-2-211-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-2111100000000000
χ214444444-41-211-2-2-4-41-211-2-211-2-21111-2-2-2-2-1-1-1-12222-1-1-1-12222-1-1-1-1222200000000000
χ224444444-4-21-2-211-4-4-21-2-211-2-211-2-2-2-211112222-1-1-1-12222-1-1-1-12222-1-1-1-100000000000
χ23444-2-2-2-241-2−1−3i32−1+3i3211-2-21-211-2-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i3211111111-2-2-2-2−1−3i32−1−3i32−1+3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i32111100000000000
χ24444-2-2-2-241-2−1+3i32−1−3i3211-2-21-211-2-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i3211111111-2-2-2-2−1+3i32−1+3i32−1−3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i32111100000000000
χ25444-2-2-2-24-2111−1−3i32−1+3i32-2-2-21-2-21111−1−3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-211111111−1−3i32−1−3i32−1+3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i3200000000000
χ26444-2-2-2-24-2111−1+3i32−1−3i32-2-2-21-2-21111−1+3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-211111111−1+3i32−1+3i32−1−3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i3200000000000
χ27444-2-2-2-2-41-2−1−3i32−1+3i3211221-211-2-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i321111-1-1-1-122221+3i321+3i321−3i321−3i32-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-100000000000
χ28444-2-2-2-2-41-2−1+3i32−1−3i3211221-211-2-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i321111-1-1-1-122221−3i321−3i321+3i321+3i32-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-100000000000
χ29444-2-2-2-2-4-2111−1−3i32−1+3i3222-21-2-21111−1−3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i322222-1-1-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-11+3i321+3i321−3i321−3i3200000000000
χ30444-2-2-2-2-4-2111−1+3i32−1−3i3222-21-2-21111−1+3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i322222-1-1-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-11−3i321−3i321+3i321+3i3200000000000
χ3144-44-4-4401-211-2-2001-2-1-12211-2-2-1-1-1-1222233-3-3000033-3-30000-3-333000000000000000
χ3244-44-4-4401-211-2-2001-2-1-12211-2-2-1-1-1-12222-3-3330000-3-333000033-3-3000000000000000
χ3344-44-4-440-21-2-21100-2122-1-1-2-2112222-1-1-1-1000033-3-3000033-3-30000-3-33300000000000
χ3444-44-4-440-21-2-21100-2122-1-1-2-2112222-1-1-1-10000-3-3330000-3-333000033-3-300000000000
χ3544-4-222-201-2−1−3i32−1+3i3211−2i32i31-2-1-122−1−3i32−1+3i32111+3i321+3i321−3i321−3i32-1-1-1-133-3-30000−3−i32−3−i323−i323−i32i3i3i3i33+i323+i32−3+i32−3+i32−i3−i3−i3−i300000000000
χ3644-4-222-201-2−1−3i32−1+3i32112i3−2i31-2-1-122−1−3i32−1+3i32111+3i321+3i321−3i321−3i32-1-1-1-1-3-33300003+i323+i32−3+i32−3+i32−i3−i3−i3−i3−3−i32−3−i323−i323−i32i3i3i3i300000000000
χ3744-4-222-201-2−1+3i32−1−3i3211−2i32i31-2-1-122−1+3i32−1−3i32111−3i321−3i321+3i321+3i32-1-1-1-1-3-33300003−i323−i32−3−i32−3−i32i3i3i3i3−3+i32−3+i323+i323+i32−i3−i3−i3−i300000000000
χ3844-4-222-201-2−1+3i32−1−3i32112i3−2i31-2-1-122−1+3i32−1−3i32111−3i321−3i321+3i321+3i32-1-1-1-133-3-30000−3+i32−3+i323+i323+i32−i3−i3−i3−i33−i323−i32−3−i32−3−i32i3i3i3i300000000000
χ3944-4-222-20-2111−1−3i32−1+3i32−2i32i3-2122-1-111−1−3i32−1+3i32-1-1-1-11+3i321+3i321−3i321−3i32000033-3-3i3i3i3i3−3−i32−3−i323−i323−i32−i3−i3−i3−i33+i323+i32−3+i32−3+i3200000000000
χ4044-4-222-20-2111−1−3i32−1+3i322i3−2i3-2122-1-111−1−3i32−1+3i32-1-1-1-11+3i321+3i321−3i321−3i320000-3-333−i3−i3−i3−i33+i323+i32−3+i32−3+i32i3i3i3i3−3−i32−3−i323−i323−i3200000000000
χ4144-4-222-20-2111−1+3i32−1−3i32−2i32i3-2122-1-111−1+3i32−1−3i32-1-1-1-11−3i321−3i321+3i321+3i320000-3-333i3i3i3i33−i323−i32−3−i32−3−i32−i3−i3−i3−i3−3+i32−3+i323+i323+i3200000000000
χ4244-4-222-20-2111−1+3i32−1−3i322i3−2i3-2122-1-111−1+3i32−1−3i32-1-1-1-11−3i321−3i321+3i321+3i32000033-3-3−i3−i3−i3−i3−3+i32−3+i323+i323+i32i3i3i3i33−i323−i32−3−i32−3−i3200000000000
χ434-40400-401-211-2-200-123-300-1-1223-33-30000−i3i3−i3i300−2i32i3−i3i3−i3i300−2i32i3−i3i3−i3i3−2i32i30000000000000
χ444-40400-401-211-2-200-123-300-1-1223-33-30000i3−i3i3−i3002i3−2i3i3−i3i3−i3002i3−2i3i3−i3i3−i32i3−2i30000000000000
χ454-40400-401-211-2-200-12-3300-1-122-33-330000−i3i3i3−i3−2i32i300−i3i3i3−i3−2i32i300i3−i3−i3i300−2i32i300000000000
χ464-40400-401-211-2-200-12-3300-1-122-33-330000i3−i3−i3i32i3−2i300i3−i3−i3i32i3−2i300−i3i3i3−i3002i3−2i300000000000
χ474-40400-4044444400-4-40000-4-4-4-40000000000000000000000000000000000000000000
χ484-40400-40-21-2-211002-1003-322-1-100003-33-300−2i32i3−i3i3i3−i300−2i32i3−i3i3i3−i3−2i32i300i3−i3−i3i300000000000
χ494-40400-40-21-2-211002-1003-322-1-100003-33-3002i3−2i3i3−i3−i3i3002i3−2i3i3−i3−i3i32i3−2i300−i3i3i3−i300000000000
χ504-40400-40-21-2-211002-100-3322-1-10000-33-33−2i32i300i3−i3i3−i3−2i32i300i3−i3i3−i300−2i32i3i3−i3i3−i300000000000
χ514-40400-40-21-2-211002-100-3322-1-10000-33-332i3−2i300−i3i3−i3i32i3−2i300−i3i3−i3i3002i3−2i3−i3i3−i3i300000000000
χ524-40-2−2i32i3201-2−1−3i32−1+3i321100-123-3001+3i321−3i32-1-1−3−i323+i32−3+i323−i32−i3i3i3−i3−i3i3−i3i300−2i32i33+i32−3−i32−3+i323−i323-3i3−i33+i32−3−i32−3+i323−i32i3−i3-3300000000000
χ534-40-2−2i32i3201-2−1−3i32−1+3i321100-123-3001+3i321−3i32-1-1−3−i323+i32−3+i323−i32−i3i3i3−i3i3−i3i3−i3002i3−2i3−3−i323+i323−i32−3+i32-33−i3i3−3−i323+i323−i32−3+i32−i3i33-300000000000
χ544-40-2−2i32i3201-2−1+3i32−1−3i321100-12-33001−3i321+3i32-1-13−i32−3+i323+i32−3−i32−i3i3i3−i3−i3i3i3−i3−2i32i300−3+i323−i32−3−i323+i32i3−i3-333−i32−3+i323+i32−3−i323-3i3−i300000000000
χ554-40-2−2i32i3201-2−1+3i32−1−3i321100-12-33001−3i321+3i32-1-13−i32−3+i323+i32−3−i32−i3i3i3−i3i3−i3−i3i32i3−2i3003−i32−3+i323+i32−3−i32−i3i33-3−3+i323−i32−3−i323+i32-33−i3i300000000000
χ564-40-2−2i32i32044-2-2-2-200-4-400002222−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000
χ574-40-2−2i32i320-2111−1−3i32−1+3i32002-100-33-1-11+3i321−3i32i3−i3−i3i33+i32−3−i323−i32−3+i32−2i32i300i3−i3i3−i3i3−i3-33−3−i323+i323−i32−3+i323-3i3−i3−3−i323+i323−i32−3+i3200000000000
χ584-40-2−2i32i320-2111−1−3i32−1+3i32002-100-33-1-11+3i321−3i32i3−i3−i3i33+i32−3−i323−i32−3+i322i3−2i300−i3i3−i3i3−i3i33-33+i32−3−i32−3+i323−i32-33−i3i33+i32−3−i32−3+i323−i3200000000000
χ594-40-2−2i32i320-2111−1+3i32−1−3i32002-1003-3-1-11−3i321+3i32i3−i3−i3i3−3+i323−i32−3−i323+i3200−2i32i3−i3i3i3−i33-3i3−i3−3+i323−i32−3−i323+i32i3−i3-333−i32−3+i323+i32−3−i3200000000000
χ604-40-2−2i32i320-2111−1+3i32−1−3i32002-1003-3-1-11−3i321+3i32i3−i3−i3i3−3+i323−i32−3−i323+i32002i3−2i3i3−i3−i3i3-33−i3i33−i32−3+i323+i32−3−i32−i3i33-3−3+i323−i32−3−i323+i3200000000000
χ614-40-22i3−2i3201-2−1−3i32−1+3i321100-12-33001+3i321−3i32-1-13+i32−3−i323−i32−3+i32i3−i3−i3i3−i3i3i3−i3−2i32i3003+i32−3−i323−i32−3+i32i3−i33-3−3−i323+i32−3+i323−i32-33i3−i300000000000
χ624-40-22i3−2i3201-2−1−3i32−1+3i321100-12-33001+3i321−3i32-1-13+i32−3−i323−i32−3+i32i3−i3−i3i3i3−i3−i3i32i3−2i300−3−i323+i32−3+i323−i32−i3i3-333+i32−3−i323−i32−3+i323-3−i3i300000000000
χ634-40-22i3−2i3201-2−1+3i32−1−3i321100-123-3001−3i321+3i32-1-1−3+i323−i32−3−i323+i32i3−i3−i3i3−i3i3−i3i300−2i32i3−3+i323−i323+i32−3−i32-33i3−i3−3+i323−i323+i32−3−i32i3−i33-300000000000
χ644-40-22i3−2i3201-2−1+3i32−1−3i321100-123-3001−3i321+3i32-1-1−3+i323−i32−3−i323+i32i3−i3−i3i3i3−i3i3−i3002i3−2i33−i32−3+i32−3−i323+i323-3−i3i33−i32−3+i32−3−i323+i32−i3i3-3300000000000
χ654-40-22i3−2i32044-2-2-2-200-4-4000022222i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000
χ664-40-22i3−2i320-2111−1−3i32−1+3i32002-1003-3-1-11+3i321−3i32−i3i3i3−i3−3−i323+i32−3+i323−i3200−2i32i3−i3i3i3−i3-33i3−i33+i32−3−i323−i32−3+i32i3−i33-3−3−i323+i32−3+i323−i3200000000000
χ674-40-22i3−2i320-2111−1−3i32−1+3i32002-1003-3-1-11+3i321−3i32−i3i3i3−i3−3−i323+i32−3+i323−i32002i3−2i3i3−i3−i3i33-3−i3i3−3−i323+i32−3+i323−i32−i3i3-333+i32−3−i323−i32−3+i3200000000000
χ684-40-22i3−2i320-2111−1+3i32−1−3i32002-100-33-1-11−3i321+3i32−i3i3i3−i33−i32−3+i323+i32−3−i32−2i32i300i3−i3i3−i3i3−i33-33−i32−3+i32−3−i323+i32-33i3−i33−i32−3+i32−3−i323+i3200000000000
χ694-40-22i3−2i320-2111−1+3i32−1−3i32002-100-33-1-11−3i321+3i32−i3i3i3−i33−i32−3+i323+i32−3−i322i3−2i300−i3i3−i3i3−i3i3-33−3+i323−i323+i32−3−i323-3−i3i3−3+i323−i323+i32−3−i3200000000000

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