Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#11961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| prime radical | C2×C11×#493 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,17,15,16,18,19)(20,21,23,26,25,29,22,30,24,27,31,34,32,35,33,28);(13,16)(14,18)(21,26)(22,31)(23,33)(25,32)(27,34)(28,29)(30,35);(13,16)(17,19)(21,27)(26,34)(28,30)(29,35)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4949);