Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | D11×#2639 |
| Fitting | C11×#2639 ⋊ C2 |
| Sylow | C11 ⋊ C2×#2639 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D11 |
| commutator, socle, cosocle | C23×C11 | C25 |
| Fitting | C11×#2639 | C2 |
| prime radical | C2×D11×#121 | C2 |
| hypercenter | #2639 | D11 |
| hypocenter | C11 | C2×#2639 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #2639 | |
3326 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 336000);