Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#10623257 |
| Fitting | C22×C11×C4⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ C22×#547 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D11 |
| commutator, cosocle | C22×C11 | C26 |
| Frattini | C22 | C25×D11 |
| Fitting | C22×C11×C4⋊Q8 | C2 |
| socle | C24×C11 | C24 |
| hypercenter | C22×C4⋊Q8 | D11 |
| hypocenter | C11 | C22×#547 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊Q8 | |
12230 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1076514);