Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33671 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29)(30,40)(31,37)(32,38)(33,36)(34,48)(35,42)(39,47)(41,55)(43,54)(44,50)(45,52)(46,53)(49,58)(51,57)(56,59);(21,24)(25,27)(28,30,32,42)(29,35,38,40)(31,41,34,44)(33,43,46,58)(36,49,53,54)(37,50,48,55)(39,51,52,56)(45,57,47,59);(29,36)(31,34)(33,47)(35,49)(37,39)(38,53)(40,54)(41,44)(43,59)(45,46)(48,52)(50,51)(55,56)(57,58);(20,22,23,26)(21,25,24,27)(28,31,32,34)(29,37,38,48)(30,41,42,44)(33,45,46,47)(35,50,40,55)(36,52,53,39)(43,57,58,59)(49,56,54,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26659);