Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C7 |
| direct product | D5×C11×#3862 |
| unambiguous semidirect product | C5⋊(C2×C11×#3862) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D5×#3862 |
| commutator, cosocle, hypocenter | C5×C72 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C2×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C11 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1155 |
836 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#15668773, C11⋊#15668773, C11×#15668768, … |
| maximal normal subgroup of | C11×#15668773, C11⋊#15668773, C11×#15668768, … |
| maximal quotient of | C11×Dic5×#3862, C2×D5×C11×#3862 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 106);