Finite Group DatabasebetaFinite Group Databasebeta| order | 723 |
| isoclinism | isoclinic class of C241⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C241⋊C3 |
| Fitting, socle, derived, Sylow | C241 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C241 | C3 |
| LCS | G ▷ C241 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 241 |
| transitive degree | μt(G) = 241 |
Polycyclic presentation:
3,241|b^a=b^1583 conjugacy classes — view the full character table.
| maximal subgroup of | D241⋊C3, C2×C241⋊C3, C3×C241⋊C3, … |
| maximal normal subgroup of | D241⋊C3, C2×C241⋊C3, C3×C241⋊C3, … |
| maximal quotient of | C2×C241⋊C3, C241⋊C9, C3×C241⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(723, 1);