Finite Group DatabasebetaFinite Group Databasebeta| order | 27468 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×Dic327 |
| unambiguous semidirect product | C3⋊(C3×C7×Dic109) |
| derived | C3×C109 ⋊ C3×C4×C7 |
| Hall | C32×C7×C109 ⋊ C4 |
| Hall | C32×C109 ⋊ C4×C7 |
| Hall | C7×C109 ⋊ C3×Dic3 |
| Sylow | C109 ⋊ C3×C7×Dic3 |
| Hall | C32×C7 ⋊ Dic109 |
| Sylow | C32 ⋊ C7×Dic109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | D327 |
| commutator, hypocenter | C3×C109 | C3×C4×C7 |
| Frattini | C2 | C3×C7×D327 |
| Fitting, socle, prime radical | C2×C32×C7×C109 | C2 |
| cosocle | C2×C3×C109 | C2×C3×C7 |
| LCS | G ▷ C3×C109 | |
| UCS | C1 ◁ C2×C3×C7 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9156 |
6930 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27468, 132);