Finite Group DatabasebetaFinite Group Databasebeta| order | 15650 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C313 · Schur multiplier (H2) = C5 |
| direct product | C5⋊D5×C313 |
| unambiguous semidirect product | C5⋊(D5×C313) |
| Fitting, socle, Hall | C52×C313 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C313 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C313 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C2×C313 |
| Frattini | C1 | G |
| Fitting, socle | C52×C313 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C313 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7825 |
4382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D52×C313, (C5⋊D5)⋊D313, C5⋊D5×D313, … |
| maximal normal subgroup of | D52×C313, (C5⋊D5)⋊D313, C5⋊D5×D313, … |
| maximal quotient of | #1039×C313, C2×C5⋊D5×C313 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15650, 7);