Finite Group DatabasebetaFinite Group Databasebeta| order | 22336 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C349 ⋊ C2 |
| Sylow | C349 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D349 |
| commutator, socle, cosocle | C2×C349 | C25 |
| Fitting | H(5,𝔽2)×C349 | C2 |
| hypercenter | H(5,𝔽2) | D349 |
| hypocenter | C349 | #585 |
| LCS | G ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
810 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5584 |
Polycyclic presentation:
2^6,349|e^2=f,b^a=bf,d^a=df,c^b=cf,g^e=g^3482992 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22336, 1384);