Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#8200 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C4 | C2×C4×C8×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C23×C11 | C4×D4 |
| prime radical | C22×D4×C11 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(17,21)(18,19)(22,23)(24,25,27,30,28,26,29,31);(13,15)(16,17,19,23,20,22,18,21);(17,22)(21,23)(24,26,27,31,28,25,29,30)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1188);