Finite Group DatabasebetaFinite Group Databasebeta| order | 16430 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C53 · Schur multiplier (H2) = C1 |
| direct product | C5×C53×D31 |
| Fitting, socle, Hall | C5×C31×C53 ⋊ C2 |
| derived, Sylow | C31 ⋊ C2×C5×C53 |
| Hall | C31×C53 ⋊ C2×C5 |
| Hall | C5×C31 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C53 | D31 |
| commutator, cosocle, hypocenter | C31 | C2×C5×C53 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C53 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C53 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8215 |
4505 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D31×D53, D5×C53×D31, D31×D265, … |
| maximal normal subgroup of | C5×D31×D53, D5×C53×D31, D31×D265, … |
| maximal quotient of | C5×C53×Dic31, C2×C5×C53×D31 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16430, 4);