Finite Group DatabasebetaFinite Group Databasebeta| order | 14910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D71⋊C7 |
| unambiguous semidirect product | (C5×D71)⋊(C3×C7) |
| unambiguous semidirect product | (C3×C5×D71)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D71⋊C7 |
| commutator, cosocle, hypocenter | C71 | C2×C3×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C71 | C2×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C3×C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1065 |
285 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×D71⋊C7, C5×D3×D71⋊C7, D15×D71⋊C7, … |
| maximal normal subgroup of | C3×D5×D71⋊C7, C5×D3×D71⋊C7, D15×D71⋊C7, … |
| maximal quotient of | C3×C5×Dic71⋊C7, C2×C3×C5×D71⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14910, 22);