Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#22537 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C4×Q8×C11 ◁ G | |
1002 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(18,19)(20,21,23,27,24,26,30,33)(22,25,28,32,29,31,34,35);(12,13,16,17)(14,18,15,19)(20,22,24,29)(21,25,26,31)(23,28,30,34)(27,32,33,35);(12,14,16,15)(13,18,17,19)(21,26)(23,30)(25,31)(28,34);(12,15,16,14)(13,18,17,19)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15525);