Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C2×C11×#2401 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C11 | C23 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| socle | C24×C11 | C24 |
| prime radical | C25×C11 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C11 ◁ G | |
2294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37);(3,4)(5,8)(6,7)(9,10)(11,12,14,16)(13,15,17,18)(19,20,22,24)(21,23,25,26);(4,7)(8,10)(11,13,14,17)(12,15,16,18)(19,21)(20,23)(22,25)(24,26);(12,16)(15,18)(21,25)(23,26);(3,5,6,9)(4,8,7,10)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27537);