Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17524 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C22×C22⋊C4 |
| prime radical | C19×#3482 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C4×#41×C19 ◁ G | |
936 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)(21,25)(22,28)(23,30)(26,33)(27,31)(32,34)(36,37,40,44,41,43,39,48)(38,45,46,42,47,51,49,50);(20,21,24,27)(22,26,28,34)(23,31,30,25)(29,33,35,32)(36,38,41,47)(37,42,43,50)(39,49,40,46)(44,51,48,45);(20,22)(21,26)(23,29)(24,28)(25,32)(27,34)(30,35)(31,33)(37,43)(42,50)(44,48)(45,51);(22,28)(26,34)(29,35)(32,33)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10512);