Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C23×C4⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ #20909 |
2258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4288 |
Polycyclic presentation:
2^8,67|a^2=g,b^2=eg,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^66,e^b=eh,g^b=gh2704 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 170796);