Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C67×#2646 ⋊ C2 |
| Sylow | C67 ⋊ #36998 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D67 |
| commutator, socle, cosocle | C23×C67 | C25 |
| Fitting | C67×#2646 | C2 |
| prime radical | C22×C22⋊D67 | C23 |
| hypercenter | #2646 | D67 |
| hypocenter | C67 | #36998 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #2646 | |
1526 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8576 |
Polycyclic presentation:
2^8,67|a^2=f,b^2=g,c^2=fh,d^2=g,b^a=bf,c^a=cg,d^a=df,e^a=efh,c^b=ch,d^b=dfh,i^b=i^66,i^c=i^661108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 384097);