Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13215 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#13215 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1961 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C11×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,25)(15,30,34,39)(16,28)(17,22)(18,24)(19,23)(20,33,38,36)(21,26)(27,32,37,42)(29,35)(31,40,43,41);(12,14,26,24,17,29,35,22,18,21,25,13,19,28,16,23)(15,31,40,39,33,37,32,38,34,43,41,30,36,27,42,20);(12,15,18,34)(13,20)(14,27)(16,32,35,42)(17,33,19,36)(21,37)(22,30)(23,39)(24,38)(25,40,26,41)(28,43)(29,31)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6203);