Finite Group DatabasebetaFinite Group Databasebeta| order | 16330 |
| isoclinism | isoclinic class of D115 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D115 |
| unambiguous semidirect product | C5⋊(D23×C71) |
| unambiguous semidirect product | C23⋊(D5×C71) |
| Fitting, socle, Hall | C5×C23×C71 ⋊ C2 |
| derived, Hall | C5×C23 ⋊ C2×C71 |
| Hall | C23×C71 ⋊ D5 |
| Hall | C5×C71 ⋊ D23 |
| Sylow | C23 ⋊ D5×C71 |
| Sylow | C5 ⋊ D23×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D115 |
| commutator, cosocle, hypocenter | C5×C23 | C2×C71 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C71 | C2 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C71 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8165 |
4189 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D71×D115, D5×D23×C71, D115⋊D71, … |
| maximal normal subgroup of | D71×D115, D5×D23×C71, D115⋊D71, … |
| maximal quotient of | C71×Dic115, C2×C71×D115 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16330, 8);