Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33428 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | #117 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C2×#432 |
| prime radical | C2×#41×C19 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C19×#405 ◁ G | |
528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(20,21,23,29,24,30,36,47,25,28,37,43,38,44,50,51)(22,31,33,45,34,41,49,46,32,26,35,39,48,27,40,42);(20,22)(21,26)(23,35)(24,34)(25,32)(27,30)(28,31)(29,45)(33,37)(36,40)(38,48)(39,43)(41,44)(42,51)(46,47)(49,50);(20,22)(21,27,28,41)(23,35)(24,34)(25,32)(26,30,31,44)(29,46,43,42)(33,37)(36,40)(38,48)(39,51,45,47)(49,50);(22,32)(26,31)(27,41)(33,35)(34,48)(39,45)(40,49)(42,46)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26416);