Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7654 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#9901 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C43×C11 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,16)(17,19)(20,21,22,26,23,25,27,24)(28,29,31,34,32,33,35,30);(13,16)(17,18)(21,24)(22,27)(25,26)(28,30,31,33,32,34,35,29);(12,14,15,19)(13,17,16,18)(21,25)(24,26)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2889);