Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C23 |
| direct product | C2×C11×#1327 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #99 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C2×M16 | C23×C11 |
| socle | C22×C11 | #324 |
| prime radical | C24×C11 | M16 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C22×C4×C11 ◁ C22×C11×M16 ◁ G | |
410 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29);(3,4,6,11,7,10,15,17,8,12,14,18,5,9,13,16);(4,9,12,10)(6,14)(11,16,18,17)(13,15)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4443);