Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12715 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#12715 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1781 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×#41 | C23×C19 |
| prime radical | C19×#3500 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×C19×2−1+4 ◁ G | |
976 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)(22,31,34,44)(23,28,35,26)(24,29)(25,30)(27,33,42,37)(32,47)(36,43,50,40)(38,45)(39,49)(41,51)(46,48);(21,26)(23,35)(27,39)(28,30)(29,40)(31,46)(32,48)(36,50)(41,42)(43,45)(44,47)(49,51);(20,22)(21,27)(23,32)(24,37)(25,34)(26,39)(28,41)(29,44)(30,42)(31,45)(33,38)(35,48)(36,51)(40,47)(43,46)(49,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5703);