Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33557 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C11 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G | |
1258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,19)(16,20)(17,22)(21,26)(23,25)(24,27);(12,14)(13,17)(15,22)(16,21)(18,19)(20,25)(23,24)(26,27);(12,14)(13,18)(15,23)(16,21)(17,19)(20,26)(22,24)(25,27);(14,21)(17,25)(18,26)(22,23)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26545);