Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11033 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #394 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1438 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1264 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(22,30,33,26)(23,34,36,27)(24,38)(25,28)(29,41)(31,42)(32,43,39,46)(35,51)(37,45,40,47)(44,50)(48,49);(20,22)(21,26)(23,35)(24,39)(25,33)(27,44)(28,30)(29,46)(31,37)(32,41)(34,51)(36,50)(38,43)(40,49)(42,45)(47,48);(20,23)(21,27)(22,31)(24,40)(25,36)(26,42)(28,34)(29,47)(30,48)(32,50)(33,49)(35,39)(37,41)(38,45)(43,51)(44,46)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4021);