Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18319 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C25×C19 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1058 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)(22,31,34,44)(23,35,38,28)(25,30,39,27)(26,36,42,32)(33,46,49,47)(37,43,51,45)(40,48,41,50);(20,22,24,34)(21,26,29,42)(23,36,38,32)(25,33,39,49)(27,40,30,41)(28,44,35,31)(37,50,51,48)(43,46,45,47);(23,37)(28,45)(31,46)(32,48)(35,43)(36,50)(38,51)(44,47);(21,27)(26,40)(28,43)(29,30)(31,47)(35,45)(41,42)(44,46)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11307);