Finite Group DatabasebetaFinite Group Databasebeta| order | 605 |
| isoclinism | isoclinic class of C121⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C121⋊C5 |
| Fitting, derived, Sylow | C121 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C121 | C5 |
| Frattini, socle | C11 | C11⋊C5 |
| LCS | G ▷ C121 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 121 |
Polycyclic presentation:
5,11^2|b^11=c,b^a=b^4c^7,c^a=c^429 conjugacy classes — view the full character table.
| maximal subgroup of | D121⋊C5, C2×C121⋊C5, C3×C121⋊C5, … |
| maximal normal subgroup of | D121⋊C5, C2×C121⋊C5, C3×C121⋊C5, … |
| maximal quotient of | C2×C121⋊C5, C3×C121⋊C5, C121⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(605, 1);