Finite Group DatabasebetaFinite Group Databasebeta| order | 32046 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C49×C109 ⋊ C2×C3 |
| Hall | #30630916 ⋊ C2 |
| Hall | C49×D109 ⋊ C3 |
| Hall | D109 ⋊ C49⋊C3 |
| Sylow | C109 ⋊ C2×C49⋊C3 |
| Sylow | C49 ⋊ D109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C109 | C2×C3 |
| Frattini | C7 | #17987078 |
| socle | C7×C109 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C49×C109 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5341 |
Polycyclic presentation:
2,3,7,109,7|c^7=e^2,d^a=d^108,c^b=c^2e,d^b=d^63,e^b=e^2920 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32046, 15);