Finite Group DatabasebetaFinite Group Databasebeta| order | 15330 |
| isoclinism | isoclinic class of D73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D73⋊C3 |
| unambiguous semidirect product | D73⋊(C3×C5×C7) |
| unambiguous semidirect product | (C73⋊C3)⋊(C2×C5×C7) |
| unambiguous semidirect product | (C5×D73)⋊(C3×C7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C2×C3×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C73 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C5×C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2555 |
630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×#64408⋊C3, C5×#20259505, C5×D7×D73⋊C3, … |
| maximal normal subgroup of | C5×C7×#64408⋊C3, C5×#20259505, C5×D7×D73⋊C3, … |
| maximal quotient of | C5×C7×Dic73⋊C3, C2×C5×C7×D73⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15330, 21);