Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D87⋊D29 |
| Fitting, socle, derived, Hall | C3×C292 ⋊ C22 |
| Sylow | C292 ⋊ C2×D3 |
| Sylow | C3 ⋊ D292 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C292 | C22 |
| LCS | G ▷ C3×C292 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,29^2|c^a=c^2,d^a=d^28,d^b=d^28,e^b=e^28678 conjugacy classes — view the full character table.
| maximal subgroup of | #29502829⋊C2, D261⋊D29, ((C29⋊D29)⋊C3)⋊D3, … |
| maximal normal subgroup of | C3×D87⋊D29 |
| maximal quotient of | D261⋊D29, C3×D87⋊D29, D87⋊D87, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 40);