Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#11709 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C2×#102 |
| prime radical | C19×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
450 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)(28,29,31,36,34,39,33,38)(30,40,43,54,44,57,41,56)(32,46,45,37,49,53,48,55)(35,47,51,42,52,58,50,59);(20,22)(21,24)(23,27)(25,26)(28,30)(29,35)(31,41)(32,47)(33,43)(34,44)(36,50)(37,54)(38,51)(39,52)(40,53)(42,48)(45,59)(46,57)(49,58)(55,56);(28,31,34,33)(29,36,39,38)(30,41,44,43)(32,45,49,48)(35,50,52,51)(37,53,55,46)(40,56,57,54)(42,47,59,58)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4697);