Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#13136 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #459 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C22×C11×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(17,20)(18,26)(19,21)(23,28)(24,25)(27,29)(30,31);(12,14,15,13)(16,17,21,24,22,25,19,20)(18,23,30,31,28,26,27,29);(16,18,19,27,22,28,21,30)(17,23,20,29,25,26,24,31)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6124);