Finite Group DatabasebetaFinite Group Databasebeta| order | 14910 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C71 · Schur multiplier (H2) = C1 |
| direct product | C7×D15×C71 |
| unambiguous semidirect product | C3⋊(C7×D5×C71) |
| unambiguous semidirect product | C5⋊(D3×C7×C71) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C71 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C7×C71 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C71 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C7×C71 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7455 |
4473 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D15×D71, D7×D15×C71, D15×D497, … |
| maximal normal subgroup of | C7×D15×D71, D7×D15×C71, D15×D497, … |
| maximal quotient of | C7×Dic15×C71, C2×C7×D15×C71 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14910, 18);