Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C3⋊D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C32 |
| direct product | C5×C3⋊D32 |
| Fitting, socle, Hall | C34×C5 ⋊ C22 |
| derived, Sylow | C34 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D32 |
| commutator, cosocle, hypocenter | C34 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C34×C5 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C5 | |
712 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C3⋊D32, C5×#10620215, #72254849, … |
| maximal normal subgroup of | D5×C3⋊D32, C5×#10620215, #72254849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 461);