Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9415 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9415 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 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)(22,29,30,33)(23,26,31,32)(24,27)(25,28)(34,35)(36,37)(38,41,45,50)(39,42)(40,43)(44,47)(46,48,51,49);(20,22,24,32,25,30,34,26)(21,23,27,33,28,31,35,29)(36,38)(37,41,43,50)(39,46)(40,45)(42,48,44,49)(47,51);(20,23)(21,26)(22,27)(24,33)(25,31)(28,32)(29,34)(30,35)(37,42)(39,47)(41,48)(43,44)(46,51)(49,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2403);