Finite Group DatabasebetaFinite Group Databasebeta| order | 15550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D5×C311⋊C5 |
| unambiguous semidirect product | C5⋊(C2×C311⋊C5) |
| unambiguous semidirect product | (D5×C311)⋊C5 |
| Fitting, socle, derived | C5×C311 ⋊ C2×C5 |
| Hall | C5×C311⋊C5 ⋊ C2 |
| Sylow | C311 ⋊ C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C311 | C2×C5 |
| LCS | G ▷ C5×C311 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1555 |
268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C311⋊C5)⋊AGL(1,𝔽5), AGL(1,𝔽5)×C311⋊C5, D5×D311⋊C5, … |
| maximal normal subgroup of | (C311⋊C5)⋊AGL(1,𝔽5), AGL(1,𝔽5)×C311⋊C5, D5×D311⋊C5, … |
| maximal quotient of | Dic5×C311⋊C5, C2×D5×C311⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15550, 10);