Finite Group DatabasebetaFinite Group Databasebeta| order | 27468 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×#89137⋊C3 |
| unambiguous semidirect product | #89137⋊(C32×C7) |
| unambiguous semidirect product | (C3×#89137)⋊(C3×C7) |
| Fitting, socle | C3×C7×C109 ⋊ C3×C4 |
| derived, Sylow | C109 ⋊ C32×C4×C7 |
| Hall | C3×C7×C109⋊C3 ⋊ C4 |
| Hall | C7×#89137 ⋊ C32 |
| Hall | C3×C109⋊C3 ⋊ C4×C7 |
| Hall | C7×C109 ⋊ C32×C4 |
| Hall | #89137 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | #89137⋊C3 |
| commutator, hypocenter | C109 | C32×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C109 | C3×C4 |
| prime radical | C3×C7×D109⋊C3 | C2 |
| cosocle | D109 | C2×C32×C7 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C3×C7 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2289 |
441 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27468, 162);