Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| isoclinism | isoclinic class of D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C72×D55 |
| unambiguous semidirect product | (C2×C5)⋊(C72×D11) |
| unambiguous semidirect product | (C2×C11)⋊(C72×D5) |
| Fitting, socle | C2×C5×C72×C11 ⋊ C2 |
| derived, Hall | C5×C11 ⋊ C22×C72 |
| Hall | C5×C72×C11 ⋊ C22 |
| Hall | C72×C11 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C72×D5 |
| Sylow | C5 ⋊ C2×C72×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D55 |
| commutator, cosocle, hypocenter | C5×C11 | C22×C72 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72×C11 | C2 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C2×C72 | |
200 conjugacy classes of subgroups.
2842 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 108);