Finite Group DatabasebetaFinite Group Databasebeta| order | 724 |
| isoclinism | isoclinic class of #10624382 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C181 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C181 | C4 |
| prime radical, cosocle | D181 | C2 |
| LCS | G ▷ C181 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 181 |
Polycyclic presentation:
2^2,181|a^2=b,c^a=c^162,c^b=c^18049 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10624382, #10624382⋊C3, C3×#10624382, … |
| maximal normal subgroup of | C2×#10624382, #10624382⋊C3, C3×#10624382, … |
| maximal quotient of | #13089685, C2×#10624382, C3×#10624382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(724, 3);