Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C67×#2440 ⋊ C2 |
| Sylow | C67 ⋊ #36781 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D67 |
| commutator, socle, cosocle | C23×C67 | C25 |
| Fitting | C67×#2440 | C2 |
| prime radical | #22563643 | C2 |
| hypercenter | #2440 | D67 |
| hypocenter | C67 | #36781 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #2440 | |
1690 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8576 |
Polycyclic presentation:
2^8,67|b^2=f,c^2=f,d^2=g,b^a=bf,c^a=cg,d^a=df,e^a=efh,i^a=i^66,c^b=ch,d^b=dfh,i^c=i^66,i^d=i^661306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 378064);