Finite Group DatabasebetaFinite Group Databasebeta| order | 36414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#19104522 |
| Fitting, socle, Hall | C7×C172 ⋊ D9 |
| derived, Hall | C7×#14579585 ⋊ C2 |
| Hall | #14579585 ⋊ D7 |
| Sylow | C172 ⋊ D63 |
| Sylow | C7 ⋊ #19104522 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×#14579585 | C2 |
| Fitting, socle | C7×C172 | D9 |
| LCS | G ▷ C7×#14579585 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1071 |
Polycyclic presentation:
2,3,7,3,17^2|b^3=d,b^a=b^2d^2,c^a=c^6,d^a=d^2,e^a=ef^12,f^a=f^16,e^b=e^5f^13,f^b=e^6f^9,e^d=e^9f^2,f^d=e^14f^7169 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36414, 73);