Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23874 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1674 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)(14,19)(15,26)(16,18)(17,22)(20,27)(21,29)(23,38)(24,33)(25,35)(28,37)(30,32)(31,36)(34,39)(40,42)(41,43);(13,18)(16,29)(19,33)(20,26)(21,22)(24,30)(27,31)(32,35)(34,38)(36,37)(39,41)(42,43);(12,14,17,25)(13,19,22,35)(15,23,28,40)(16,30,29,24)(18,32,21,33)(20,34,36,43)(26,42,37,38)(27,41,31,39);(12,15)(13,20)(14,23)(16,31)(17,28)(18,26)(19,34)(21,37)(22,36)(24,41)(25,40)(27,29)(30,39)(32,42)(33,38)(35,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16862);