Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23994 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24287 |
| 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 | |
1298 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)(15,30)(16,34)(17,24)(18,23)(19,25)(20,28)(21,32)(22,31)(27,38)(29,43)(33,39)(35,42)(36,40)(37,41);(12,14,17,28,19,29,18,36)(13,20,23,26,25,40,24,43)(15,31,32,35,33,27,37,16)(21,38,30,42,41,22,39,34);(12,15)(13,21)(14,27)(16,28)(17,32)(18,37)(19,33)(20,38)(22,40)(23,30)(24,39)(25,41)(26,42)(29,31)(34,43)(35,36);(12,16,17,31,19,35,18,27)(13,22,23,34,25,38,24,42)(14,15,28,32,29,33,36,37)(20,39,26,21,40,30,43,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17275);