Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2121 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#12574 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#99 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C22×D4 | C23×C19 |
| prime radical | C23×D4×C19 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C24×C19 ◁ C23×D4×C19 ◁ G | |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25)(26,32)(27,35,36,30)(28,31)(29,34,37,39)(33,38);(20,21,22,23)(24,26)(25,29)(27,34)(28,33)(30,32)(31,37)(35,38)(36,39);(26,33)(29,37)(32,38)(34,39)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5562);