Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#17412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#120 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C19×#117 ◁ G | |
1046 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)(20,21,23,28,25,29,34,41)(22,27,31,40,30,39,42,49)(24,26,33,37,35,38,45,48)(32,36,44,47,43,46,50,51);(21,26)(23,33)(27,36)(29,38)(31,44)(34,45)(39,46)(42,50);(20,22,24,32)(21,27,26,36)(23,31,33,44)(25,30,35,43)(28,40,37,47)(29,39,38,46)(34,42,45,50)(41,49,48,51);(22,30)(27,39)(31,42)(32,43)(36,46)(40,49)(44,50)(47,51)1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10400);