Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#10590410 |
| Fitting | C32×C4×C22⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ C4×B(4,𝔽2) |
4432 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 18 points:
(1,2,3)(4,5,6)(7,8,9,10);(2,3)(5,6)(12,16);(11,13)(12,15,16,17)(14,18);(5,6)(11,12,14,16)(13,17,18,15)192 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((1,2,3)(4,5,6)(7,8,9,10), (2,3)(5,6)(12,16), (11,13)(12,15,16,17)(14,18), (5,6)(11,12,14,16)(13,17,18,15));