Finite Group DatabasebetaFinite Group Databasebeta| order | 12780 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C71 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D5×C71 |
| unambiguous semidirect product | C5⋊(C22×C32×C71) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C32×C71) |
| Fitting, socle | C2×C32×C5×C71 ⋊ C2 |
| derived, Sylow | C5 ⋊ C22×C32×C71 |
| Hall | C32×C5×C71 ⋊ C22 |
| Hall | C5×C71 ⋊ C22×C32 |
| Hall | C32×C5 ⋊ C22×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C71 | D5 |
| commutator, cosocle, hypocenter | C5 | C22×C32×C71 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C71 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C32×C71 | |
120 conjugacy classes of subgroups.
5112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12780, 117);