Finite Group DatabasebetaFinite Group Databasebeta| order | 22336 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D349⋊C32 |
| derived, Sylow | C349 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #13063703 |
| commutator, hypocenter | C349 | C2×C32 |
| Frattini | C8 | C2×#13063703 |
| Fitting | C16×C349 | C4 |
| socle | C2×C349 | C2×C16 |
| prime radical | C2×D349 | C16 |
| cosocle | #19150208 | C22 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11168 |
Polycyclic presentation:
2^6,349|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^213,g^b=g^348,g^c=g^3481456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22336, 1480);