Finite Group DatabasebetaFinite Group Databasebeta| order | 13650 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C13 · Schur multiplier (H2) = C5 |
| direct product | C52×C13×D21 |
| unambiguous semidirect product | C3⋊(C52×C13×D7) |
| unambiguous semidirect product | C7⋊(C52×D3×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C13 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C2×C52×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C13 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C52×C13 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6825 |
3900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D13×D21, C52×D3×C13×D7, C52×D21⋊D13, … |
| maximal normal subgroup of | C52×D13×D21, C52×D3×C13×D7, C52×D21⋊D13, … |
| maximal quotient of | C52×C13×Dic21, C2×C52×C13×D21 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13650, 151);