Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×#11716325 |
| Fitting, socle | C2×C72×C19 ⋊ C2×C3 |
| derived | C7×C19 ⋊ C22×C3×C7 |
| Hall | C2×C7×D7×C19 ⋊ C3 |
| Hall | C7×#87704 ⋊ C22 |
| Hall | C72×C19 ⋊ C22×C3 |
| Hall | C2×C7×D7 ⋊ C19⋊C3 |
| Sylow | C72 ⋊ C22×C19⋊C3 |
| Sylow | C19 ⋊ C2×C7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | #11716325 |
| commutator, cosocle, hypocenter | C7×C19 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C2×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C2×C7 | |
84 conjugacy classes of subgroups.
518 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 213);