Finite Group DatabasebetaFinite Group Databasebeta| order | 17324 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C71⋊#6923 |
| Fitting, socle, derived, Hall | C61×C71 ⋊ C4 |
| Sylow | C71 ⋊ #6923 |
| Sylow | C61 ⋊ Dic71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C61×C71 | C4 |
| prime radical, cosocle | C71×D61 | C2 |
| LCS | G ▷ C61×C71 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4331 |
Polycyclic presentation:
2^2,61,71|a^2=b,c^a=c^50,d^a=d^70,c^b=c^601139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17324, 7);