Finite Group DatabasebetaFinite Group Databasebeta| order | 12460 |
| isoclinism | isoclinic class of D89 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C7×D89 |
| unambiguous semidirect product | C89⋊(C22×C5×C7) |
| unambiguous semidirect product | (C2×C89)⋊(C2×C5×C7) |
| Fitting, socle | C2×C5×C7×C89 ⋊ C2 |
| derived, Sylow | C89 ⋊ C22×C5×C7 |
| Hall | C5×C7×C89 ⋊ C22 |
| Hall | C7×C89 ⋊ C22×C5 |
| Hall | C5×C89 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C7 | D89 |
| commutator, cosocle, hypocenter | C89 | C22×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C89 | C2 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C2×C5×C7 | |
40 conjugacy classes of subgroups.
3220 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×ΓL(1,𝔽8)×D89, C5×D3×C7×D89, C2×C3×C5×C7×D89, … |
| maximal normal subgroup of | C2×C5×ΓL(1,𝔽8)×D89, C2×C3×C5×C7×D89 |
| maximal quotient of | C5×D3×C7×D89, C2×C3×C5×C7×D89, C2×C5×C7×D267 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12460, 35);