Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23995 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24288 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2408 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
1290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,26)(15,31)(16,34)(17,24)(18,23)(19,25)(20,29)(21,33)(22,35)(27,38)(28,43)(30,42)(32,39)(36,41)(37,40);(12,14,17,29,19,30,18,32)(13,20,23,26,25,39,24,42)(15,27,33,16,28,35,37,36)(21,22,31,34,40,38,43,41);(12,15)(13,21)(14,27)(16,29)(17,33)(18,37)(19,28)(20,38)(22,39)(23,31)(24,43)(25,40)(26,41)(30,35)(32,36)(34,42);(12,16,17,35,19,36,18,27)(13,22,23,34,25,38,24,41)(14,28,29,37,30,15,32,33)(20,31,26,40,39,43,42,21)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17276);