Finite Group DatabasebetaFinite Group Databasebeta| order | 8850 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C59 · Schur multiplier (H2) = C5 |
| direct product | C59×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C5⋊D5)⋊(C3×C59) |
| unambiguous semidirect product | (C5⋊D5×C59)⋊C3 |
| Fitting, socle, Hall | C52×C59 ⋊ C2×C3 |
| derived, Sylow | C52 ⋊ C2×C3×C59 |
| Hall | C59×C52⋊C3 ⋊ C2 |
| Hall | C5⋊D5×C59 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C2×C59 |
| Hall | C5⋊D5 ⋊ C3×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | (C5⋊D5)⋊C3 |
| commutator, hypocenter | C52 | C2×C3×C59 |
| Frattini | C1 | G |
| Fitting, socle | C52×C59 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C59 | |
24 conjugacy classes of subgroups.
590 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8850, 12);