Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×#1181 |
| unambiguous semidirect product | D29⋊(C2×C3×C4) |
| Fitting, socle | C22×C3×C29 ⋊ C4 |
| derived, Sylow | C29 ⋊ C22×C3×C4 |
| Hall | C3×C29 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #1181 |
| commutator, hypocenter | C29 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C29 | C4 |
| prime radical | C22×C3×D29 | C2 |
| cosocle | D29 | C23×C3 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C22×C3 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 348 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3×AGL(1,𝔽29), C22×D3×#1181, C2×C3×C4×#1181, … |
| maximal normal subgroup of | C22×C3×AGL(1,𝔽29), C22×D3×#1181, C2×C3×C4×#1181, … |
| maximal quotient of | C2×C3×C4×#1181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 190);