Finite Group DatabasebetaFinite Group Databasebeta| order | 10230 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16811786 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C31 | C2×C5 |
| LCS | G ▷ C3×C11×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,11,31|b^a=b^2,d^a=d^10,e^a=e^30,d^c=d^4,e^c=e^2117 conjugacy classes — view the full character table.
| maximal subgroup of | #16811774⋊D3, #16811780⋊D3, D3×#16811786, … |
| maximal normal subgroup of | #16811774⋊D3, #16811780⋊D3, D3×#16811786, … |
| maximal quotient of | C3⋊#20291885, C2×C3⋊#16811786, C9⋊#16811786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10230, 71);