Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C8×C11×#99 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | C4×C22⋊C4 |
| prime radical | C22×D4×C11 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ C23×C8×C11 ◁ G | |
614 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,3,4,5,6,7,8)(17,18,19,20,21,22,23,24,25,26,27);(9,10)(11,15,16,13)(12,14);(9,11)(10,13)(12,16)(14,15)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1147);