Finite Group DatabasebetaFinite Group Databasebeta| order | 34688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C271 ⋊ C2 |
| Sylow | C271 ⋊ #3484 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D271 |
| commutator, socle, cosocle | C22×C271 | C25 |
| Fitting | C2×H(5,𝔽2)×C271 | C2 |
| hypercenter | C2×H(5,𝔽2) | D271 |
| hypocenter | C271 | #3484 |
| LCS | G ▷ C22×C271 ▷ C271 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
1900 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4336 |
Polycyclic presentation:
2^7,271|b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^2704634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34688, 18141);