Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C4×C3⋊#272 |
| Fitting | C3×C4×H(3,𝔽3) ⋊ C2 |
| derived, Sylow | C3×H(3,𝔽3) ⋊ C2×C4 |
383 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #13047675, #13047676, #13047687, … |
| maximal normal subgroup of | #13047675, #13047676, #13047687, … |
| maximal quotient of | C8×C3⋊#272, #13048003, C4×C3⋊#1084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 508);