Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | C7⋊D7×D57 |
| Fitting, socle, derived, Hall | C3×C72×C19 ⋊ C22 |
| Hall | C72×C19 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×D57 |
| Sylow | C19 ⋊ D3×C7⋊D7 |
| Sylow | C3 ⋊ D19×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C19 | C22 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
780 conjugacy classes — view the full character table.
| maximal subgroup of | C7⋊D7×D171, #45692307, #45692308, … |
| maximal normal subgroup of | #45692307, #45692308, D57×ΓL(1,𝔽8)⋊D7, … |
| maximal quotient of | C7⋊D7×D171, C3×C7⋊D7×D57, D57×C3⋊(C7⋊D7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 279);