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) = C22 |
| direct product | C19×#11934 |
| 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 | C23×C19 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
306 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)(21,24)(22,26)(25,27)(28,29,33,39,34,40,49,56,35,41,47,54,31,37,32,38)(30,42,45,53,43,55,44,57,46,58,48,36,50,52,59,51);(20,21,23,25)(22,27,26,24)(28,30)(29,36)(31,43)(32,48)(33,44)(34,50)(35,46)(37,51)(38,55)(39,42)(40,57)(41,53)(45,49)(47,59)(52,56)(54,58);(28,31,35,34)(29,37,41,40)(30,43,46,50)(32,47,49,33)(36,51,53,57)(38,54,56,39)(42,55,58,52)(44,48,59,45)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4922);