Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C2×C11×#2034 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C11 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#121 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ C24×C4×C11 ◁ G | |
2006 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29);(8,9)(11,12)(13,15)(14,16)(17,18);(3,4)(5,6)(7,8)(9,10)(12,15)(16,17);(4,6)(7,9,10,8)(12,16)(14,18)(15,17)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16465);