Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C72 · Schur multiplier (H2) = C7 |
| direct product | C5×C72×D33 |
| unambiguous semidirect product | C3⋊(C5×C72×D11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C72 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C2×C5×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C11 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C5×C72 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8085 |
4410 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×C72×D11, C5×C7×D7×D33, C5×C7×D21⋊D11, … |
| maximal normal subgroup of | C5×D3×C72×D11, C5×C7×D7×D33, C5×C7×D21⋊D11, … |
| maximal quotient of | C5×C72×Dic33, C2×C5×C72×D33 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 126);