Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×(C19⋊C3)⋊Dic13 |
| unambiguous semidirect product | (C19⋊C3)⋊(C3×Dic13) |
| derived, Hall | C13×C19 ⋊ C32×C4 |
| Hall | C3×C13×C19⋊C3 ⋊ C4 |
| Hall | Dic247 ⋊ C32 |
| Hall | C3×C19⋊C3 ⋊ Dic13 |
| Sylow | C19 ⋊ C32×Dic13 |
| Sylow | C13 ⋊ C3×(C19⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | (C19⋊C3)⋊D13 |
| commutator, hypocenter | C13×C19 | C32×C4 |
| Frattini | C2 | C3×(C19⋊C3)⋊D13 |
| Fitting, socle | C2×C3×C13×C19 | C2×C3 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C2×C3 | |
72 conjugacy classes of subgroups.
378 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 104);