Finite Group DatabasebetaFinite Group Databasebeta| order | 588 |
| isoclinism | isoclinic class of C22⋊#3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#3861 |
| Fitting, socle, derived, Hall | C22×C72 ⋊ C3 |
| Sylow | C72 ⋊ A4 |
| Sylow | C22 ⋊ #3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C72 | C3 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 196 |
Polycyclic presentation:
3,2^2,7^2|b^a=bc,c^a=b,d^a=d^2,e^a=e^268 conjugacy classes — view the full character table.
| maximal subgroup of | #11924338, #11924340, C2×C22⋊#3861, … |
| maximal normal subgroup of | #11924338, #11924340, C2×C22⋊#3861, … |
| maximal quotient of | Q8⋊#3861, C2×C22⋊#3861, C22⋊#89204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(588, 59);