Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18494 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C2×#120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
944 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,29)(23,27)(24,32)(25,28)(26,30)(31,34)(33,35)(36,37)(38,44)(39,43)(40,45)(41,46)(42,47)(48,51)(49,50);(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32)(36,38,42,49)(37,43,47,51)(39,40,48,41)(44,46,50,45);(36,39)(37,44)(38,40)(41,49)(42,48)(43,46)(45,51)(47,50);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(36,40,42,41)(37,45,47,46)(38,48,49,39)(43,44,51,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11482);