Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | Dic7×#87704 |
| derived, Hall | C72×C19 ⋊ C3×C4 |
| Hall | C7×C19×Dic7 ⋊ C3 |
| Hall | C7×#87704 ⋊ C4 |
| Hall | C7×Dic7 ⋊ C19⋊C3 |
| Sylow | C72 ⋊ C4×C19⋊C3 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×#87704 |
| commutator, hypocenter | C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C72×C19 | C2×C3 |
| prime radical | C2×C7×#87704 | C2 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
52 conjugacy classes of subgroups.
470 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊C4×#87704, #45691766, #45691769, … |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊C4×#87704, #45691766, #45691769, … |
| maximal quotient of | Dic7×#11924776, C3×Dic7×#87704, Dic21×#87704 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 114);