Finite Group DatabasebetaFinite Group Databasebeta| order | 22336 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C8×D349 |
| Fitting | C22×C8×C349 ⋊ C2 |
| derived, Sylow | C349 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D349 |
| commutator, hypocenter | C349 | C23×C8 |
| Frattini | C4 | C23×D349 |
| Fitting | C22×C8×C349 | C2 |
| socle | C23×C349 | C2×C4 |
| prime radical | C23×D349 | C4 |
| cosocle | C4×C349 | C24 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11168 |
5632 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22336, 1305);