Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12753 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#12753 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1790 |
| commutator | C2×D4 | C22×C4×C19 |
| Frattini, cosocle | C22×D4 | C23×C19 |
| prime radical | C19×#3532 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C23×C19 ◁ C22×D4×C19 ◁ G | |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28)(23,31,32,26)(24,27)(25,29,33,35)(30,34);(20,22)(21,25)(23,29)(24,30)(26,28)(27,33)(31,34)(32,35);(26,31)(28,34)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5741);