Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊(C19⋊#5997) |
| unambiguous semidirect product | C19⋊(C3⋊#5997) |
| Fitting, socle, derived, Hall | C3×C72×C19 ⋊ C4 |
| Hall | C72×C19 ⋊ Dic3 |
| Hall | C3×C72 ⋊ Dic19 |
| Hall | C3×C19 ⋊ #5997 |
| Sylow | C72 ⋊ Dic57 |
| Sylow | C19 ⋊ C3⋊#5997 |
| Sylow | C3 ⋊ C19⋊#5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C19 | C4 |
| prime radical, cosocle | C3×C19×C7⋊D7 | C2 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7^2,19|a^2=b,c^a=c^2,d^a=d^4e^6,e^a=d^3e^3,f^a=f^18,d^b=d^6,e^b=e^6744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 290);