Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊#1181 |
| unambiguous semidirect product | (C2×#1181)⋊D3 |
| Hall | C3×C29 ⋊ C22⋊C4 |
| Sylow | C29 ⋊ (C2×D3)⋊C4 |
| Sylow | C3 ⋊ C22⋊#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#1181 |
| commutator, Fitting, socle | C2×C3×C29 | C2×C4 |
| prime radical | C2×D3×D29 | C2 |
| cosocle | C2×C3×D29 | C22 |
| hypocenter | C3×C29 | C22⋊C4 |
| LCS | G ▷ C2×C3×C29 ▷ C3×C29 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 348 |
Polycyclic presentation:
2^4,3,29|a^2=c,b^a=bd,f^a=f^12,e^b=e^2,f^c=f^2860 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 90);