Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D32×D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D32×D21 |
| Fitting, socle, derived, Hall | C33×C7 ⋊ C23 |
| Sylow | C33 ⋊ C22×D7 |
| Sylow | C7 ⋊ D33 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C33×C7 | C23 |
| LCS | G ▷ C33×C7 | |
| UCS | C1 | |
324 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 84 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D33×D7, D32×C3⋊AGL(1,𝔽7), D3×D212, … |
| maximal normal subgroup of | D33×D7, D32×C3⋊AGL(1,𝔽7) |
| maximal quotient of | D3×D212, #72230568 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 838);