Finite Group DatabasebetaFinite Group Databasebeta| order | 588 |
| isoclinism | isoclinic class of C49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×C49⋊C3 |
| unambiguous semidirect product | (C4×C49)⋊C3 |
| Fitting, Hall | C4×C49 ⋊ C3 |
| derived, Sylow | C49 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C49⋊C3 |
| commutator, hypocenter | C49 | C3×C4 |
| Frattini, socle | C2×C7 | C2×ΓL(1,𝔽8) |
| Fitting | C4×C49 | C3 |
| prime radical | C2×C49⋊C3 | C2 |
| cosocle | C2×C49 | C2×C3 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C4 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 196 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | (C49⋊C3)⋊C8, C8×C49⋊C3, (C49⋊C3)⋊Q8, … |
| maximal normal subgroup of | (C49⋊C3)⋊C8, C8×C49⋊C3, (C49⋊C3)⋊Q8, … |
| maximal quotient of | C8×C49⋊C3, C2×C4×C49⋊C3, C4×C49⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(588, 2);