Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#21780 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2308 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3486 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29,25,28,39,43)(22,30,33,44,32,26,37,41)(23,34,35,45,36,27,38,42)(31,40,48,50,47,46,49,51);(20,22)(21,26)(23,31)(24,37)(25,32)(27,40)(28,30)(29,44)(33,39)(34,46)(35,49)(36,47)(38,48)(41,43)(42,51)(45,50);(26,30)(40,46)(41,44)(50,51);(20,23,25,36)(21,27,28,34)(22,31,32,47)(24,38,39,35)(26,40,30,46)(29,45,43,42)(33,49,37,48)(41,51,44,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14768);