Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C4×C3⋊((C3⋊D3)⋊C3) |
| Fitting | C3×C4×H(3,𝔽3) ⋊ C2 |
| derived | C33 ⋊ C2×C3×C4 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×C4 |
253 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 253 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) = 108 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #88785⋊C3, #88788⋊C3, #13047668, … |
| maximal normal subgroup of | #88785⋊C3, #88788⋊C3, #13047668, … |
| maximal quotient of | C8×C3⋊((C3⋊D3)⋊C3), #13047897, C4×C3⋊((C3⋊Dic3)⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 477);