Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D55×C49⋊C3 |
| unambiguous semidirect product | C5⋊(D11×C49⋊C3) |
| unambiguous semidirect product | C11⋊(D5×C49⋊C3) |
| unambiguous semidirect product | (C49×D55)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C11×C49 | C2×C3 |
| Frattini | C7 | ΓL(1,𝔽8)×D55 |
| socle | C5×C7×C11 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C5×C11×C49 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2695 |
551 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D55×D49⋊C3, D55⋊(D49⋊C3), D5×D11×C49⋊C3, … |
| maximal normal subgroup of | D55×D49⋊C3, D55⋊(D49⋊C3), D5×D11×C49⋊C3, … |
| maximal quotient of | C49⋊C3×Dic55, C2×D55×C49⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 31);