Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#11495 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×C22⋊C4 |
| commutator | C23 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C2×C22⋊C8 |
| prime radical | C23×C19 | C22×C8 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(22,28,30,25)(23,26)(24,27)(29,34,35,32)(31,33)(36,37,40,46,42,43,49,50,41,45,48,51,38,47,39,44);(20,22,24,30)(21,25,27,28)(23,29,31,35)(26,32,33,34)(36,38,41,42)(37,43,45,47)(39,40,49,48)(44,51,50,46);(20,23,24,31)(21,26,27,33)(22,29,30,35)(25,32,28,34)(36,39,38,48,41,49,42,40)(37,44,47,51,45,50,43,46)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4483);