Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2×C7 |
| unambiguous semidirect product | C22⋊(C19⋊#3862) |
| unambiguous semidirect product | C19⋊(C22⋊#3862) |
| Fitting, socle, derived, Hall | C22×C72×C19 ⋊ C3 |
| Hall | C72×C19 ⋊ A4 |
| Hall | C22×C72 ⋊ C19⋊C3 |
| Hall | C22×C19 ⋊ #3862 |
| Sylow | C72 ⋊ C22⋊(C19⋊C3) |
| Sylow | C19 ⋊ C22⋊#3862 |
| Sylow | C22 ⋊ C19⋊#3862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C72×C19 | C3 |
| LCS | G ▷ C22×C72×C19 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
3,2^2,7^2,19|b^a=c,c^a=bc,d^a=d^4,e^a=e^2,f^a=f^71244 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 291);