Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C19 ⋊ C22×C3 |
| Hall | D7×D133 ⋊ C3 |
| Hall | C19⋊#3862 ⋊ C22 |
| Sylow | C72 ⋊ C2×D19⋊C3 |
| Sylow | C19 ⋊ #64422⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C19 | C22×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7^2,19|e^a=e^6,f^a=f^18,d^b=d^6,d^c=d^2,e^c=e^4,f^c=f^11124 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#11716327, #45692034, #45692040, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#11716327, #45692034, #45692040, … |
| maximal quotient of | #45691559, C3×#26013900, #45692452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 162);