Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23360 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2380 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
688 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)(15,26,29,40)(16,20)(17,21)(19,28,36,42)(23,34)(24,37,30,33)(27,32)(31,35)(38,41)(39,43);(12,14)(13,18)(15,27)(16,30)(17,25)(19,34)(20,37)(21,22)(23,28)(24,31)(26,38)(29,41)(32,40)(33,35)(36,43)(39,42);(12,15,16,28,17,29,31,42)(13,19,35,40,21,36,20,26)(14,23,24,27,25,39,30,41)(18,32,37,34,22,38,33,43);(13,20,21,35)(18,33,22,37)(19,26,36,40)(32,43,38,34)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16348);