Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19086 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19090 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18)(15,16)(19,26)(20,21)(22,24)(25,27)(28,29)(30,36)(31,39)(32,34)(33,38)(35,40)(37,43)(41,42);(12,13,17,21)(14,19,23,27)(15,18,16,20)(22,25,24,26)(31,40)(35,39)(36,43)(38,41);(12,14)(13,19)(15,22)(16,24)(17,23)(18,25)(20,26)(21,27)(28,30)(29,33)(31,41)(32,37)(34,42)(35,43)(36,39)(38,40);(12,15,17,16)(13,20,21,18)(14,22,23,24)(19,26,27,25)(29,34)(33,42)(35,39)(36,43)341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12078);