Finite Group DatabasebetaFinite Group Databasebeta| order | 32754 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D103⋊C3 |
| unambiguous semidirect product | D103⋊(C3×C53) |
| unambiguous semidirect product | (C103⋊C3)⋊(C2×C53) |
| unambiguous semidirect product | (C53×D103)⋊C3 |
| Fitting, socle, Hall | C53×C103 ⋊ C2×C3 |
| derived, Sylow | C103 ⋊ C2×C3×C53 |
| Hall | C53×C103⋊C3 ⋊ C2 |
| Hall | C53×D103 ⋊ C3 |
| Hall | C103⋊C3 ⋊ C2×C53 |
| Hall | D103 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D103⋊C3 |
| commutator, cosocle, hypocenter | C103 | C2×C3×C53 |
| Frattini | C1 | G |
| Fitting, socle | C53×C103 | C2×C3 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C53 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5459 |
1219 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32754, 10);