Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11178 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #388 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1440 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
820 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 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)(22,32)(23,37,41,45)(24,30)(25,29)(26,31)(27,34)(28,39,46,40)(33,48,50,42)(35,43)(36,47)(38,51,49,44);(20,22)(21,27)(23,38)(24,35)(25,34)(26,36)(28,44)(29,47)(30,32)(31,43)(33,40)(37,48)(39,50)(41,49)(42,45)(46,51);(20,23,24,39,26,41,25,40)(21,28,29,45,31,46,30,37)(22,33,34,49,36,50,35,38)(27,42,32,44,43,48,47,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4166);