Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×C22⋊#3861 |
| unambiguous semidirect product | C22⋊(C19×#3861) |
| Fitting, socle, Hall | C22×C72×C19 ⋊ C3 |
| derived, Hall | C22×C72 ⋊ C3×C19 |
| Hall | C72×C19 ⋊ A4 |
| Hall | C22×C19 ⋊ #3861 |
| Sylow | C72 ⋊ A4×C19 |
| Sylow | C22 ⋊ C19×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C22⋊#3861 |
| commutator, cosocle, hypocenter | C22×C72 | C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C19 | C3 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C19 | |
100 conjugacy classes of subgroups.
1292 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8), #45692504, #45692505, … |
| maximal normal subgroup of | C19×ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8), #45692504, #45692505, … |
| maximal quotient of | C19×C22⋊#89204, C3×C19×C22⋊#3861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 298);