Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18519 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C2×#120 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
914 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)(20,21,24,27)(22,28,30,35)(23,31,33,26)(25,32,34,29)(36,37,42,47)(38,44,49,50)(39,43,48,51)(40,45,41,46);(20,22,24,30)(21,25,27,34)(23,32,33,29)(26,35,31,28)(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);(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, 11507);