Finite Group DatabasebetaFinite Group Databasebeta| order | 10371 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3457⋊C3 |
| Fitting, socle, derived, Sylow | C3457 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3457 | C3 |
| LCS | G ▷ C3457 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
3,3457|b^a=b^7221155 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3457⋊C3, C2×C3457⋊C3, #44527482, … |
| maximal normal subgroup of | D3457⋊C3, C2×C3457⋊C3, #44527482, … |
| maximal quotient of | C2×C3457⋊C3, #44527480, C3×C3457⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10371, 1);