Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C2×C42 |
| direct product | C19×#7858 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×C42 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | C2×#95 |
| prime radical | C24×C19 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ G | |
592 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)(22,28,30,34)(23,26)(24,27)(25,29,32,35)(31,33)(36,37,40,44,41,45,39,43)(38,42,46,49,47,50,48,51);(20,22)(21,25,27,32)(23,29)(24,30)(26,28,33,34)(31,35)(36,38)(37,42)(39,48)(40,46)(41,47)(43,51)(44,49)(45,50);(36,39,41,40)(37,43,45,44)(38,46,47,48)(42,49,50,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 846);