Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| isoclinism | isoclinic class of D3×#1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | Dic3×#1181 |
| unambiguous semidirect product | (C3×#1181)⋊C4 |
| unambiguous semidirect product | (C3⋊#1181)⋊C4 |
| derived, Hall | C3×C29 ⋊ C42 |
| Sylow | C29 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ C4×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#1181 |
| commutator, hypocenter | C3×C29 | C42 |
| Fitting, socle | C2×C3×C29 | C2×C4 |
| prime radical, cosocle | C2×C3×D29 | C22 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 348 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×AGL(1,𝔽29), C4×D3×#1181, C2×Dic3×#1181 |
| maximal normal subgroup of | Dic3×AGL(1,𝔽29), C4×D3×#1181, C2×Dic3×#1181 |
| maximal quotient of | C2×Dic3×#1181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 89);