Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C2×C11×#3315 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C2×C11×#547 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G | |
2126 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)(11,12,16,19)(13,20,21,26)(14,18,15,23)(17,24,25,22);(3,5)(4,7)(6,10)(8,9)(13,21)(17,25)(20,26)(22,24);(11,13)(12,17)(14,22)(15,24)(16,21)(18,26)(19,25)(20,23);(5,10)(7,9)(11,14,16,15)(12,18,19,23)(13,22,21,24)(17,26,25,20)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54122);