Finite Group DatabasebetaFinite Group Databasebeta| order | 9975 |
| isoclinism | isoclinic class of #87705 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#87705 |
| Fitting, Hall | C7×C19×C25 ⋊ C3 |
| derived, Hall | C7×C19 ⋊ C3×C25 |
| Hall | C19×C25 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C25 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×C25 |
| Sylow | C7 ⋊ C25×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #87705 |
| commutator, hypocenter | C7×C19 | C3×C25 |
| Frattini | C5 | C5×#87705 |
| Fitting | C7×C19×C25 | C3 |
| socle, cosocle | C5×C7×C19 | C3×C5 |
| prime radical | C5×#87705 | C5 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
1175 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C25×#87705, C25×#11716322, C25×#11716326, … |
| maximal normal subgroup of | C2×C25×#87705, C25×#11716322, C25×#11716326, … |
| maximal quotient of | C2×C25×#87705, C25×#11924777, C3×C25×#87705 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9975, 4);