Finite Group DatabasebetaFinite Group Databasebeta| order | 655 |
| isoclinism | isoclinic class of C131⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C131⋊C5 |
| Fitting, socle, derived, Sylow | C131 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C131 | C5 |
| LCS | G ▷ C131 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 131 |
Polycyclic presentation:
5,131|b^a=b^5331 conjugacy classes — view the full character table.
| maximal subgroup of | D131⋊C5, C2×C131⋊C5, C3×C131⋊C5, … |
| maximal normal subgroup of | D131⋊C5, C2×C131⋊C5, C3×C131⋊C5, … |
| maximal quotient of | C2×C131⋊C5, C3×C131⋊C5, C131⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(655, 1);