Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊GL(2,𝔽3) |
| Fitting | Q8×C29 ⋊ D3 |
| derived | SL(2,𝔽3)×C29 ⋊ C2 |
| Sylow | C29 ⋊ GL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4⋊D29 |
| commutator, cosocle, hypocenter | SL(2,𝔽3)×C29 | C2 |
| Fitting | Q8×C29 | D3 |
| socle | C2×C29 | S4 |
| LCS | G ▷ SL(2,𝔽3)×C29 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2,3,29,2^3|d^2=f,e^2=f,b^a=b^2,c^a=c^28,d^a=de,e^a=ef,d^b=e,e^b=def,e^d=ef106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 100);