Finite Group DatabasebetaFinite Group Databasebeta| order | 10900 |
| isoclinism | isoclinic class of #89137 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×#89137 |
| Fitting, socle, Hall | C52×C109 ⋊ C4 |
| derived, Sylow | C109 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | #89137 |
| commutator, hypocenter | C109 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C109 | C4 |
| prime radical | C52×D109 | C2 |
| cosocle | D109 | C2×C52 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C52 | |
48 conjugacy classes of subgroups.
775 conjugacy classes — view the full character table.
| maximal subgroup of | #89137⋊(C52⋊C3), C52⋊C3×#89137, C52×#89137⋊C3, … |
| maximal normal subgroup of | #89137⋊(C52⋊C3), C52⋊C3×#89137, C52×#89137⋊C3, … |
| maximal quotient of | C3×C52×#89137, C52×C3⋊#89137 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10900, 23);