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×#11924 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| socle | C22×C19 | C2×#102 |
| prime radical | C19×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
414 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)(20,21,22,25,23,24,26,27)(28,29)(30,40,43,56)(31,36)(32,46)(33,38)(34,39)(35,42,51,59)(37,48)(41,53,44,57)(45,55)(47,50,58,52)(49,54);(21,24)(22,26)(28,30)(29,35)(31,41)(32,47)(33,44)(34,43)(36,50)(37,53)(38,52)(39,51)(40,54)(42,45)(46,56)(48,59)(49,58)(55,57);(28,31,34,33)(29,36,39,38)(30,41,43,44)(32,45,49,48)(35,50,51,52)(37,46,55,54)(40,53,56,57)(42,58,59,47)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4912);