Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12019 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#12887 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#106 |
| 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 | |
286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(22,25)(23,24)(26,27)(28,29)(30,40,44,55)(31,46,45,59)(32,48)(33,49)(34,39)(35,43,53,56)(36,47,54,57)(37,42)(38,50)(41,52)(51,58);(21,24)(25,27)(28,30,41,56,33,45,58,47,34,44,32,43,50,31,42,57)(29,35,51,55,38,36,52,59,39,53,37,40,49,54,48,46);(20,22,23,26)(21,25,24,27)(28,31,32,47,33,30,42,43,34,45,41,57,50,44,58,56)(29,36,37,46,38,53,48,55,39,54,51,59,49,35,52,40)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5875);