Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C19 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C72×C19 ⋊ C22×C3 |
| derived, Sylow | C72 ⋊ C22×C3×C19 |
| Hall | D72×C19 ⋊ C3 |
| Hall | C7×C19×ΓL(1,𝔽8) ⋊ C22 |
| Hall | D72 ⋊ C3×C19 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C22×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D7×AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C72 | C22×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C72×C19 | C22×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C19 | |
84 conjugacy classes of subgroups.
665 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 173);