Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#17838 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C22×C4⋊C4 |
| prime radical | C2×#41×C19 | Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C4×#41×C19 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(21,25)(23,31)(26,32)(27,33)(28,35)(30,34)(36,37,40,43,41,44,39,49)(38,45,48,50,46,51,47,42);(20,21,23,25,24,27,31,33)(22,28,30,35,29,26,34,32)(36,38,39,47,41,46,40,48)(37,42,43,45,44,50,49,51);(20,22)(21,26)(23,30)(24,29)(25,32)(27,28)(31,34)(33,35)(38,46)(42,50)(45,51)(47,48);(22,29)(26,28)(30,34)(32,35)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10826);