Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#11893 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
400 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)(22,26,27,24)(23,25)(28,29,32,38,34,40,33,39)(30,41,44,57,46,58,45,55)(31,47,49,37,51,56,50,36)(35,48,52,43,54,59,53,42);(20,22)(21,24)(23,27)(25,26)(28,30)(29,35)(31,48)(32,45)(33,44)(34,46)(36,55)(37,57)(38,53)(39,52)(40,54)(41,56)(42,49)(43,50)(47,58)(51,59);(22,27)(24,26)(28,31,32,49,34,51,33,50)(29,36,39,56,40,37,38,47)(30,42,44,48,46,43,45,59)(35,41,53,55,54,58,52,57)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4881);