Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C2×C11×#2079 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 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)(11,12,15,18,16,20,14,19)(13,17,21,26,23,24,22,25);(4,7)(8,10)(11,13)(12,17)(14,22)(15,21)(16,23)(18,26)(19,25)(20,24);(3,5,6,9)(4,8,7,10)(12,18)(13,21)(14,15)(17,24)(19,20)(22,23)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16633);