Finite Group DatabasebetaFinite Group Databasebeta| order | 27468 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#20293536 |
| derived, Hall | C22×C7×C109 ⋊ C9 |
| Hall | C7×C109 ⋊ C22⋊C9 |
| Hall | C22×C109 ⋊ C7⋊C9 |
| Sylow | C109 ⋊ C22⋊(C7⋊C9) |
| Hall | C22×C7 ⋊ #11758279 |
| Sylow | C7 ⋊ C22⋊#11758279 |
| Sylow | C22 ⋊ #20293536 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊#14556233 |
| commutator, hypocenter | C22×C7×C109 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C7×C109 | C3 |
| LCS | G ▷ C22×C7×C109 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13734 |
Polycyclic presentation:
3,2^2,7,109,3|a^3=f,b^a=c,c^a=bc,d^a=d^2,e^a=e^453060 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27468, 62);