Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1364 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)(14,22,24,18)(15,19)(16,21)(17,20)(23,32,41,40)(25,38,29,33)(26,34,42,43)(27,36)(28,35)(30,39)(31,37);(12,14)(13,18)(15,26)(16,29)(17,24)(19,34)(20,22)(21,38)(23,28)(25,31)(27,42)(30,41)(32,35)(33,37)(36,43)(39,40);(12,15)(13,19)(14,23)(16,30)(17,27)(18,32)(20,36)(21,39)(22,40)(24,41)(25,42)(26,29)(28,31)(33,43)(34,38)(35,37);(12,14)(13,18)(15,23)(16,25)(17,24)(19,32)(20,22)(21,33)(26,28)(27,41)(29,31)(30,42)(34,35)(36,40)(37,38)(39,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17396);