Finite Group DatabasebetaFinite Group Databasebeta| order | 10121 |
| automorphism | ? |
| homology | Abelianization (H1) = C29 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C349⋊C29 |
| Fitting, socle, derived, Sylow | C349 ⋊ C29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C349 | C29 |
| LCS | G ▷ C349 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
29,349|b^a=b^25741 conjugacy classes — view the full character table.
| maximal subgroup of | D349⋊C29, C2×C349⋊C29, (C349⋊C3)⋊C29, … |
| maximal normal subgroup of | D349⋊C29, C2×C349⋊C29, (C349⋊C3)⋊C29, … |
| maximal quotient of | C2×C349⋊C29, C3×C349⋊C29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10121, 1);