Finite Group DatabasebetaFinite Group Databasebeta| order | 588 |
| isoclinism | isoclinic class of D7×AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Sylow | C72 ⋊ C22×C3 |
| Hall | D72 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72 | C22×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 42 |
35 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(588, 36);