Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61100 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C2×C11 | C2×D42 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
2616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,24)(15,26)(16,20)(17,21)(18,22)(19,23)(25,40)(27,29)(28,41)(30,34)(31,43)(32,37)(33,39)(35,38)(36,42);(12,14)(13,15)(16,31)(17,26)(18,34)(19,27)(20,36)(21,29)(22,24)(23,30)(25,32)(28,38)(33,41)(35,42)(37,43)(39,40);(12,15)(13,14)(16,28)(17,29)(18,24)(19,30)(20,25)(21,26)(22,34)(23,27)(31,38)(32,36)(33,43)(35,40)(37,41)(39,42);(12,16)(13,20)(14,25)(15,28)(17,32)(18,35)(19,33)(21,37)(22,38)(23,39)(24,40)(26,41)(27,42)(29,36)(30,43)(31,34);(12,17,19,18)(13,21,23,22)(14,26,27,34)(15,29,30,24)(16,32,33,35)(20,37,39,38)(25,41,42,31)(28,36,43,40)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54088);