Finite Group DatabasebetaFinite Group Databasebeta| order | 36414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C17 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C172 ⋊ C2×C9 |
| Hall | C7⋊#14579585 ⋊ C2 |
| Hall | C7×C17⋊D17 ⋊ C9 |
| Hall | C17⋊D17 ⋊ C7⋊C9 |
| Sylow | C172 ⋊ C2×C7⋊C9 |
| Sylow | C7 ⋊ #19104523 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C172 | C2×C9 |
| prime radical | C7×(C17⋊D17)⋊C3 | C3 |
| cosocle | C7×C172⋊C3 | C2×C3 |
| LCS | G ▷ C7×C172 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1071 |
Polycyclic presentation:
2,3^2,7,17^2|b^3=c,e^a=e^16,f^a=f^16,d^b=d^2,e^b=e^9f^9,f^b=e^13f^15,e^c=f^7,f^c=e^12f^16142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36414, 71);