Finite Group DatabasebetaFinite Group Databasebeta| order | 12780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C5×C3⋊D213 |
| unambiguous semidirect product | (C2×C3)⋊(C5×D213) |
| Fitting, socle | C2×C32×C5×C71 ⋊ C2 |
| derived, Hall | C32×C71 ⋊ C22×C5 |
| Hall | C32×C5×C71 ⋊ C22 |
| Hall | C5×C71 ⋊ C2×C3⋊D3 |
| Sylow | C71 ⋊ C2×C5×C3⋊D3 |
| Hall | C32×C5 ⋊ C2×D71 |
| Sylow | C32 ⋊ C2×C5×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C3⋊D213 |
| commutator, cosocle, hypocenter | C32×C71 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C71 | C2 |
| LCS | G ▷ C32×C71 | |
| UCS | C1 ◁ C2×C5 | |
120 conjugacy classes of subgroups.
3210 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12780, 110);