Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C29 |
| direct product | C2×(C29⋊D29)⋊C3 |
| unambiguous semidirect product | (C2×C29⋊D29)⋊C3 |
| Fitting, socle | C2×C292 ⋊ C2×C3 |
| derived, Sylow | C292 ⋊ C22×C3 |
| Hall | C2×C29⋊D29 ⋊ C3 |
| Hall | C292⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C29⋊D29)⋊C3 |
| commutator, cosocle, hypocenter | C292 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C292 | C2×C3 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C2 | |
70 conjugacy classes of subgroups.
292 conjugacy classes — view the full character table.
| maximal subgroup of | D3×(C29⋊D29)⋊C3, C2×C3×(C29⋊D29)⋊C3, C2×C3⋊((C29⋊D29)⋊C3) |
| maximal normal subgroup of | C2×C3×(C29⋊D29)⋊C3 |
| maximal quotient of | C2×(C29⋊D29)⋊C9, D3×(C29⋊D29)⋊C3, C2×C3×(C29⋊D29)⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 27);