Finite Group DatabasebetaFinite Group Databasebeta| order | 955 |
| isoclinism | isoclinic class of C191⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C191⋊C5 |
| Fitting, socle, derived, Sylow | C191 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C191 | C5 |
| LCS | G ▷ C191 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 191 |
| transitive degree | μt(G) = 191 |
Polycyclic presentation:
5,191|b^a=b^3943 conjugacy classes — view the full character table.
| maximal subgroup of | D191⋊C5, C2×C191⋊C5, C3×C191⋊C5, … |
| maximal normal subgroup of | D191⋊C5, C2×C191⋊C5, C3×C191⋊C5, … |
| maximal quotient of | C2×C191⋊C5, C3×C191⋊C5, C191⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(955, 1);