Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19162 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19169 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3100 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,19)(14,15,18,16)(20,21)(22,24)(23,25)(26,27);(12,14,16,13,17,18,15,19)(21,24)(25,26);(21,25)(23,27)(24,26);(12,15,17,16)(13,18,19,14)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12157);