Finite Group DatabasebetaFinite Group Databasebeta| order | 32445 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×#14524189 |
| Fitting, socle | C3×C5×C7×C103 ⋊ C3 |
| derived, Hall | C7×C103 ⋊ C32×C5 |
| Hall | C5×C7×C103 ⋊ C32 |
| Hall | C5×C103 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C103 ⋊ C3×C5×ΓL(1,𝔽8) |
| Hall | C5×C7 ⋊ C3×C103⋊C3 |
| Sylow | C7 ⋊ C3×C5×C103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #14524189 |
| commutator, cosocle, hypocenter | C7×C103 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C103 | C3 |
| LCS | G ▷ C7×C103 | |
| UCS | C1 ◁ C3×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10815 |
3645 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32445, 10);