Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊#1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3⋊#1113 |
| unambiguous semidirect product | (C2×C3)⋊#1113 |
| Fitting, socle | C2×C34 ⋊ C22 |
| derived, Sylow | C34 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊#1113 |
| commutator, cosocle, hypocenter | C34 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
630 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | #13049431, #13049444, #13049450, … |
| maximal normal subgroup of | #13049431, #13049444, #13049450, … |
| maximal quotient of | #13049704, #13049705, #13049706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 751);