Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C32 |
| direct product | C2×C3×D4×(C3⋊D3)⋊C3 |
| Fitting | C2×C3×D4×H(3,𝔽3) ⋊ C2 |
| Sylow | C3×H(3,𝔽3) ⋊ C22×D4 |
2846 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 4 generators on 18 points:
(6,7,8,9)(10,11,17)(12,14,13)(15,18,16);(1,2)(3,4,5)(11,14,15)(13,17,18);(11,13)(12,16)(14,17)(15,18);(7,9)300 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((6,7,8,9)(10,11,17)(12,14,13)(15,18,16), (1,2)(3,4,5)(11,14,15)(13,17,18), (11,13)(12,16)(14,17)(15,18), (7,9));