Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#13289 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C23×C19 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,24)(25,27)(28,29,33,40,35,41,34,39)(30,42,47,59,48,58,46,54)(31,49,43,37,50,38,32,51)(36,53,55,45,57,44,56,52);(21,24)(25,26)(28,30,43,45,34,47,31,44,35,48,32,52,33,46,50,53)(29,36,38,58,40,56,51,59,41,57,49,42,39,55,37,54);(20,22,23,27)(21,25,24,26)(28,31,33,43,35,50,34,32)(29,37,39,49,41,51,40,38)(30,44,46,45,48,53,47,52)(36,54,55,42,57,59,56,58)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6277);