Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33359 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#99 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C2×D4 | C24×C19 |
| prime radical | C19×#3498 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×D4×C19 ◁ C2×C19×H(5,𝔽2) ◁ G | |
1356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
A minimal faithful permutation representation — 4 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)(22,26)(23,27,31,25)(24,28)(29,33)(30,34,35,32);(21,25)(23,31)(26,32)(27,28)(30,35)(33,34);(20,22)(21,26)(23,30)(24,29)(25,32)(27,34)(28,33)(31,35);(22,29)(26,33)(30,35)(32,34)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26347);