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×#33373 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#99 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C2×Q8 | C24×C19 |
| prime radical | C19×#3498 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×Q8×C19 ◁ C2×C19×H(5,𝔽2) ◁ G | |
1312 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)(20,21,25,31,26,32,22,28)(23,29,34,27,24,30,33,35);(20,22,26,25)(21,27,32,35)(23,33,24,34)(28,30,31,29);(20,22,26,25)(21,28,32,31)(23,34,24,33)(27,30,35,29);(20,23,26,24)(21,29,32,30)(22,33,25,34)(27,28,35,31)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26361);