Finite Group DatabasebetaFinite Group Databasebeta| order | 27468 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C9⋊#89137) |
| unambiguous semidirect product | C9⋊(C7⋊#89137) |
| Fitting, derived, Hall | C7×C9×C109 ⋊ C4 |
| Hall | C9×C109 ⋊ Dic7 |
| Hall | C7×C109 ⋊ Dic9 |
| Sylow | C109 ⋊ Dic63 |
| Hall | C7×C9 ⋊ #89137 |
| Sylow | C9 ⋊ C7⋊#89137 |
| Sylow | C7 ⋊ C9⋊#89137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C9×C109 | C4 |
| Frattini | C3 | C3⋊(C7⋊#89137) |
| socle | C3×C7×C109 | Dic3 |
| prime radical | C3×C7×D109 | D3 |
| cosocle | C7×C9×D109 | C2 |
| LCS | G ▷ C7×C9×C109 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6867 |
Polycyclic presentation:
2^2,3,7,109,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^6,e^a=e^76,f^a=f^2,e^b=e^1081767 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27468, 55);