Finite Group DatabasebetaFinite Group Databasebeta| order | 34688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C271 ⋊ #2382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D271 |
| commutator | C22×C271 | C23×C4 |
| Fitting | #387×C271 | C2 |
| socle, prime radical, cosocle | C23×C271 | C24 |
| hypercenter | #387 | D271 |
| hypocenter | C271 | #2382 |
| LCS | G ▷ C22×C271 ▷ C271 | |
| UCS | C1 ◁ C23 ◁ #387 | |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34688 |
Polycyclic presentation:
2^7,271|a^2=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,h^c=h^270,h^d=h^2703818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34688, 7694);