Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61109 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61111 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
2600 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)(14,23)(15,27)(16,20)(17,34)(18,21)(19,26)(22,35)(24,41)(25,29)(28,30)(31,40)(32,39)(33,38)(36,43)(37,42);(12,14)(13,19)(15,21)(16,30)(17,27)(18,25)(20,37)(22,29)(23,34)(24,31)(26,35)(28,40)(32,42)(33,43)(36,39)(38,41);(12,15,18,19)(13,14,21,25)(16,28,33,36)(17,29,35,23)(20,24,38,42)(22,26,34,27)(30,40,43,39)(31,41,32,37);(12,16)(13,20)(14,24)(15,28)(17,32)(18,33)(19,36)(21,38)(22,40)(23,41)(25,42)(26,43)(27,30)(29,37)(31,35)(34,39);(13,21)(14,25)(20,38)(22,34)(24,42)(26,27)(30,43)(39,40)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54099);