Finite Group DatabasebetaFinite Group Databasebeta| order | 9072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×H(3,𝔽3)×GL(3,𝔽2) |
610 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 126 |
A minimal faithful permutation representation — 2 generators on 18 points:
(4,6)(7,8)(10,11,14)(12,15,13)(16,18,17);(1,2)(3,4,7,6,9,5,8)(10,17,18)(11,12,14)(13,15,16)132 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((4,6)(7,8)(10,11,14)(12,15,13)(16,18,17), (1,2)(3,4,7,6,9,5,8)(10,17,18)(11,12,14)(13,15,16));