Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24420 |
| 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 | |
1326 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)(12,13,16,22,18,19,17,23)(14,24,28,33,27,35,25,20)(15,29,30,37,31,21,32,36)(26,38,39,34,40,43,41,42);(13,19)(14,25)(16,17)(20,24)(21,29)(26,39)(27,28)(30,32)(33,35)(34,38)(40,41)(42,43);(12,14)(13,20)(15,26)(16,25)(17,28)(18,27)(19,33)(21,34)(22,35)(23,24)(29,42)(30,41)(31,40)(32,39)(36,38)(37,43);(12,15)(13,21)(14,26)(16,32)(17,30)(18,31)(19,29)(20,34)(22,37)(23,36)(24,38)(25,39)(27,40)(28,41)(33,42)(35,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17408);