Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#7180 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | #106 |
| commutator | C8 | C4×C8×C11 |
| Frattini, cosocle | C2×C4×C8 | C22×C11 |
| socle | C2×C11 | #1279 |
| prime radical | C23×C11 | #104 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ C2×C4×C8×C11 ◁ G | |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,22,18,24,34,39,19,25,33,21,17,23,15,32)(14,26,28,37,30,42,27,38,31,40,35,36,29,41,43,20);(12,14)(13,20,23,36,25,38,24,37)(15,27)(16,35)(17,29)(18,30)(19,31)(21,26,39,41,22,40,32,42)(28,33)(34,43)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 168);