Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C11×#1937 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C4×D4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C23×C8×C11 ◁ G | |
1114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 704 |
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)(7,8,11,15,12,16,10,13)(9,17,19,14,20,21,18,22);(8,13,16,15)(14,17,22,21);(4,6)(7,9,10,18,12,20,11,19)(8,14,15,21,16,22,13,17)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14084);