Finite Group DatabasebetaFinite Group Databasebeta| order | 15650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D1565 |
| unambiguous semidirect product | C313⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C313 ⋊ C2 |
| Sylow | C313 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D313 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C313 | C2 |
| LCS | G ▷ C52×C313 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7825 |
Polycyclic presentation:
2,5^2,313|b^a=b^4,c^a=c^4,d^a=d^3123914 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1565, C5⋊D5×D313, #44531041, … |
| maximal normal subgroup of | D5×D1565, C5⋊D5×D313, #44531041, … |
| maximal quotient of | #44531018, C2×C5⋊D1565 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15650, 6);