Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24295 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1302 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)(14,16)(15,28)(17,36)(18,23)(19,24)(20,26)(21,32)(22,34)(25,37)(27,35)(29,30)(31,39)(33,38)(40,43)(41,42);(12,14,17,26,19,27,18,22)(13,20,23,16,24,34,36,35)(15,29,31,25,33,40,32,41)(21,30,38,42,39,43,28,37);(12,15)(13,21)(14,25)(16,30)(17,31)(18,32)(19,33)(20,37)(22,29)(23,38)(24,39)(26,40)(27,41)(28,36)(34,42)(35,43);(12,16,17,34,19,35,18,20)(13,22,23,14,24,26,36,27)(15,30,31,42,33,43,32,37)(21,29,38,25,39,40,28,41)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17283);