Finite Group DatabasebetaFinite Group Databasebeta| order | 16380 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5×C7 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×C5×C7×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C5×C7 | D13 |
| commutator, cosocle, hypocenter | C13 | C22×C32×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C7×C13 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C32×C5×C7 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8190 |
5040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16380, 851);