Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of C3⋊((C5⋊D5)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C5 |
| direct product | C23×C3⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | C3⋊(C23×(C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C3⋊(C5⋊D5))⋊(C3×C23) |
| unambiguous semidirect product | (C23×C3⋊(C5⋊D5))⋊C3 |
| Fitting, socle | C3×C52×C23 ⋊ C2×C3 |
| derived | C3×C52 ⋊ C2×C3×C23 |
| Hall | C3×C23×C52⋊C3 ⋊ C2 |
| Hall | C52×C23 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ C2×C23 |
| Sylow | C52 ⋊ C3×D3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C3×C52 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C23 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C23 | |
52 conjugacy classes of subgroups.
483 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#3874⋊D3, #35208102, D23×C3⋊((C5⋊D5)⋊C3), … |
| maximal normal subgroup of | C23×#3874⋊D3, #35208102, D23×C3⋊((C5⋊D5)⋊C3), … |
| maximal quotient of | C23×C3⋊(#1039⋊C3), C2×C23×C3⋊((C5⋊D5)⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 47);