Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C2×C11×#2185 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#466 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
1178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33);(3,4)(5,6)(8,12)(9,15)(10,17)(13,22)(14,21)(16,19)(18,20);(7,8,11,14)(9,16,18,22)(10,19,17,13)(12,20,21,15);(4,6)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26500);