Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#13073541 |
| Fitting | C2×C11×#392 ⋊ C2 |
| Sylow | C11 ⋊ C2×#2539 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D11 |
| commutator, cosocle | C23×C11 | C25 |
| Frattini | C23 | C24×D11 |
| Fitting | C2×C11×#392 | C2 |
| socle | C24×C11 | C24 |
| hypercenter | C2×#392 | D11 |
| hypocenter | C11 | C2×#2539 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C2×#392 | |
5726 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
296 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 339597);