Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| isoclinism | isoclinic class of S4×D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | S4×D29 |
| unambiguous semidirect product | (S4×C29)⋊C2 |
| unambiguous semidirect product | (A4⋊D29)⋊C2 |
| unambiguous semidirect product | (A4×D29)⋊C2 |
| Fitting, socle | C22×C29 ⋊ C2×D3 |
| derived | A4×C29 ⋊ C22 |
| Sylow | C29 ⋊ C2×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C29 | C22 |
| Fitting, socle | C22×C29 | C2×D3 |
| LCS | G ▷ A4×C29 | |
| UCS | C1 | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 116 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | S4×D29⋊C7, S4×#1181 |
| maximal normal subgroup of | S4×D29⋊C7, S4×#1181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 185);