Finite Group DatabasebetaFinite Group Databasebeta| order | 10900 |
| isoclinism | isoclinic class of #89137 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#89137 |
| Fitting, Hall | C25×C109 ⋊ C4 |
| derived, Sylow | C109 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #89137 |
| commutator, hypocenter | C109 | C4×C25 |
| Frattini | C5 | C5×#89137 |
| Fitting | C25×C109 | C4 |
| socle | C5×C109 | C4×C5 |
| prime radical, cosocle | C5×D109 | C2×C5 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C25 | |
18 conjugacy classes of subgroups.
775 conjugacy classes — view the full character table.
| maximal subgroup of | C25×#89137⋊C3, C3×C25×#89137, C25×C3⋊#89137 |
| maximal normal subgroup of | C25×#89137⋊C3, C3×C25×#89137 |
| maximal quotient of | C3×C25×#89137, C25×C3⋊#89137 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10900, 6);