Finite Group DatabasebetaFinite Group Databasebeta| order | 27468 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C109 ⋊ C4×C9 |
| Hall | #20293537 ⋊ C4 |
| Hall | C7×#89137 ⋊ C9 |
| Hall | #89137 ⋊ C7⋊C9 |
| Sylow | C109 ⋊ C4×C7⋊C9 |
| Sylow | C7 ⋊ #16840981 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #22603889 |
| commutator, hypocenter | C7×C109 | C4×C9 |
| Fitting, socle | C3×C7×C109 | C3×C4 |
| prime radical, cosocle | C3×C7×D109 | C2×C3 |
| LCS | G ▷ C7×C109 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6867 |
Polycyclic presentation:
2,3,2,7,109,3|a^2=c,b^3=f,e^a=e^76,d^b=d^2,e^b=e^63,e^c=e^108249 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27468, 33);