Finite Group DatabasebetaFinite Group Databasebeta| order | 22336 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C349 ⋊ C2 |
| Sylow | C349 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D349 |
| commutator, socle | C2×C349 | C22×C8 |
| Fitting | M32×C349 | C2 |
| prime radical | #19150233 | C4 |
| cosocle | C8×C349 | C23 |
| hypercenter | M32 | D349 |
| hypocenter | C349 | #504 |
| LCS | G ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11168 |
Polycyclic presentation:
2^6,349|a^2=d,d^2=e,e^2=f,g^a=g^348,c^b=cf,g^c=g^3483520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22336, 967);