Finite Group DatabasebetaFinite Group Databasebeta| order | 10550 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C211 · Schur multiplier (H2) = C5 |
| direct product | C5⋊D5×C211 |
| unambiguous semidirect product | C5⋊(D5×C211) |
| Fitting, socle, Hall | C52×C211 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C211 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C2×C211 |
| Frattini | C1 | G |
| Fitting, socle | C52×C211 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C211 | |
32 conjugacy classes of subgroups.
2954 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D52×C211, (C5⋊D5)⋊D211, C5⋊D5×D211, … |
| maximal normal subgroup of | D52×C211, (C5⋊D5)⋊D211, C5⋊D5×D211, … |
| maximal quotient of | #1039×C211, C2×C5⋊D5×C211, C3×C5⋊D5×C211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10550, 13);