Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10793 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C4×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | C22⋊#95 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×M16×C19 ◁ G | |
1164 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)(22,27,33,42)(23,35)(24,31)(25,30)(26,29)(28,37)(32,46,48,50)(34,44,38,41)(36,45)(39,43)(40,49,51,47);(20,22,25,34,26,33,24,38)(21,27,31,41,29,42,30,44)(23,32,37,49,36,48,39,47)(28,40,35,50,43,51,45,46);(20,23)(21,28)(22,32)(24,39)(25,37)(26,36)(27,40)(29,43)(30,45)(31,35)(33,48)(34,49)(38,47)(41,50)(42,51)(44,46)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3781);