Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| derived | C3×C7 ⋊ C32×C8 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C8 |
| Sylow | C7 ⋊ C32×C3⋊C8 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #72245994, C3×C3⋊C8×AGL(1,𝔽7), #72254133, … |
| maximal normal subgroup of | #72245994, C3×C3⋊C8×AGL(1,𝔽7), #72254133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 425);