Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#32895 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
3540 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)(21,27)(22,31)(24,25)(29,44)(30,36)(32,46)(33,38)(34,37)(39,42)(40,45)(41,50)(47,48);(20,21)(22,28)(23,29)(24,36)(25,27)(26,30)(31,42)(32,41)(33,43)(34,40)(35,45)(37,44)(38,39)(46,51)(47,49)(48,50);(20,22,26,33)(21,28,30,43)(23,32,35,48)(24,31,25,38)(27,39,36,42)(29,41,45,50)(34,47,37,46)(40,49,44,51);(20,23)(21,29)(22,32)(24,37)(25,34)(26,35)(27,40)(28,41)(30,45)(31,46)(33,48)(36,44)(38,47)(39,49)(42,51)(43,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25883);