Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11246 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #391 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1441 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
624 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)(12,13,17,21,18,22,16,30)(14,23,27,33,26,39,25,19)(15,20,28,37,29,36,31,35)(24,40,41,34,42,38,43,32);(12,14,16,25,18,26,17,27)(13,19,21,23,22,33,30,39)(15,24,28,41,29,42,31,43)(20,34,35,40,36,32,37,38);(12,15,16,28,18,29,17,31)(13,20,21,35,22,36,30,37)(14,24,25,41,26,42,27,43)(19,32,23,38,33,34,39,40)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4234);