Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C2×C11×#3166 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G | |
1902 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);(3,4,6,8)(5,9,10,7)(11,12,14,16)(13,19,20,26)(15,23,22,18)(17,25,24,21);(3,5,6,10)(4,7,8,9)(12,16)(17,24)(18,23)(19,26);(11,13,15,21,14,20,22,25)(12,17,18,19,16,24,23,26);(13,20)(17,24)(19,26)(21,25)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53650);