Finite Group DatabasebetaFinite Group Databasebeta| order | 13650 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C13 · Schur multiplier (H2) = C5 |
| direct product | C7×C13×C3⋊(C5⋊D5) |
| unambiguous semidirect product | C3⋊(C7×C13×C5⋊D5) |
| unambiguous semidirect product | C5⋊(C7×C13×D15) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C13 | C3⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C3×C52 | C2×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C13 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C7×C13 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6825 |
3549 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D5×C13×D15, C7×D65⋊D15, C13×D35⋊D15, … |
| maximal normal subgroup of | C7×D5×C13×D15, C7×D65⋊D15, C13×D35⋊D15, … |
| maximal quotient of | C7×C13×C3⋊#1039, C2×C7×C13×C3⋊(C5⋊D5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13650, 145);