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 | #20293541 ⋊ C4 |
| Hall | C7×Dic109 ⋊ C9 |
| Hall | Dic109 ⋊ C7⋊C9 |
| Sylow | C109 ⋊ C4×C7⋊C9 |
| Sylow | C7 ⋊ #16840993 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #28351540 |
| commutator, hypocenter | C7×C109 | C4×C9 |
| Fitting, socle | C2×C7×C109 | C2×C9 |
| prime radical, cosocle | C2×C7×C109⋊C3 | C2×C3 |
| LCS | G ▷ C7×C109 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3052 |
Polycyclic presentation:
2,3^2,7,109,2|a^2=f,b^3=c,e^a=e^108,d^b=d^2,e^b=e^38,e^c=e^45144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27468, 86);