Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C73 ⋊ C4×C9 |
| Hall | #17987164 ⋊ C4 |
| Hall | Dic7×C73 ⋊ C9 |
| Sylow | C73 ⋊ Dic7⋊C9 |
| Hall | Dic7 ⋊ #10620323 |
| Sylow | C7 ⋊ C4×#10620323 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #22604105 |
| commutator, hypocenter | C7×C73 | C4×C9 |
| Fitting, socle | C2×C7×C73 | C2×C9 |
| prime radical, cosocle | C2×C7×C73⋊C3 | C2×C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2044 |
Polycyclic presentation:
2,3^2,7,73,2|a^2=f,b^3=c,d^a=d^6,d^b=d^2,e^b=e^4,e^c=e^64122 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 82);