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×#24410 |
| 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 | |
1322 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)(14,22,25,18)(15,27,28,19)(16,21)(17,20)(23,30,34,26)(24,33)(29,40,41,35)(31,32)(36,39)(37,42)(38,43);(12,14,17,25)(13,18,20,22)(15,24,28,39)(16,30,32,26)(19,33,27,36)(21,23,31,34)(29,42,41,38)(35,37,40,43);(12,13)(14,23)(15,19)(16,31)(17,20)(18,30)(21,32)(22,26)(24,37)(25,34)(27,28)(29,40)(33,42)(35,41)(36,38)(39,43);(12,15)(13,19)(14,24)(16,29)(17,28)(18,33)(20,27)(21,35)(22,36)(23,37)(25,39)(26,38)(30,42)(31,40)(32,41)(34,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17398);