Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#13140 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #481 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | #1926 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G | |
314 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)(12,13,18,24,16,22,19,34)(14,23,17,32,26,20,27,36)(15,28,29,39,31,43,30,35)(21,33,37,25,38,41,40,42);(12,14,19,27,16,26,18,17)(13,20,34,32,22,23,24,36)(15,25,29,41,31,42,30,33)(21,35,37,28,38,39,40,43);(12,15,18,30,16,31,19,29)(13,21,34,37,22,38,24,40)(14,25,17,33,26,42,27,41)(20,35,32,28,23,39,36,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6128);