Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | (C31⋊C3)⋊(C7⋊Dic7) |
| derived, Hall | C72×C31 ⋊ C3×C4 |
| Hall | C7⋊Dic217 ⋊ C3 |
| Hall | C72×C31⋊C3 ⋊ C4 |
| Hall | C31⋊C3 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ (C31⋊C3)⋊C4 |
| Sylow | C31 ⋊ C3×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C31⋊C3)⋊(C7⋊D7) |
| commutator, hypocenter | C72×C31 | C3×C4 |
| Fitting, socle, cosocle | C2×C72×C31 | C2×C3 |
| prime radical | C2×C72×C31⋊C3 | C2 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6076 |
Polycyclic presentation:
2,3,7^2,31,2|a^2=f,c^a=c^6,d^a=d^6,e^a=e^30,e^b=e^5646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18228, 117);