Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#18405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
1190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(14,15)(18,19)(21,24)(22,26)(25,27);(12,13)(14,17)(15,18)(16,19)(20,21)(22,27)(23,25)(24,26);(12,14,16,15)(13,17,19,18)(22,26)(24,27);(12,14,16,15)(13,18,19,17)(21,25)(24,27)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11393);