Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25×C4 |
| direct product | C11×#33559 |
| 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 ◁ C2×C4×C11 ◁ C2×C11×#41 ◁ G | |
1248 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)(15,17)(16,19)(20,26)(21,23)(22,24)(25,27);(13,17)(14,20)(18,25)(19,24)(21,27)(23,26);(14,20)(15,22)(18,26)(23,25);(12,14,16,20)(13,18,19,26)(15,21,22,27)(17,23,24,25)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26547);