Finite Group DatabasebetaFinite Group Databasebeta| order | 596 |
| isoclinism | isoclinic class of #10597010 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C149 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C149 | C4 |
| prime radical, cosocle | D149 | C2 |
| LCS | G ▷ C149 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 149 |
Polycyclic presentation:
2^2,149|a^2=b,c^a=c^105,c^b=c^14841 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10597010, C3×#10597010, C3⋊#10597010, … |
| maximal normal subgroup of | C2×#10597010, C3×#10597010, C5×#10597010, … |
| maximal quotient of | #11924753, C2×#10597010, C3×#10597010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(596, 3);