Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊(#41⋊C3) |
| unambiguous semidirect product | #90809⋊C3 |
| Hall | #90809 ⋊ C3 |
| Sylow | C29 ⋊ #41⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×D29 |
| commutator, Fitting, cosocle, hypocenter | Q8×C29 | C2×C3 |
| socle | C2×C29 | C2×A4 |
| LCS | G ▷ Q8×C29 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2,3,2^2,29,2|a^2=f,c^2=f,d^2=f,e^a=e^28,c^b=d,d^b=cd,d^c=df112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 102);