Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C29 |
| direct product | C2×#72209712 |
| Fitting | C29 ⋊ D3 |
1422789 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1422789 conjugacy classes of subgroups — too many to draw. Only its 147 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) = 24 |
A minimal faithful permutation representation — 3 generators on 18 points:
(4,6)(7,9,8,10)(11,14,12,13)(15,17,18,16);(3,4)(5,6)(8,9,10)(12,13,14)(16,17,18);(1,2)(15,16)(17,18)144 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)(7,9,8,10)(11,14,12,13)(15,17,18,16), (3,4)(5,6)(8,9,10)(12,13,14)(16,17,18), (1,2)(15,16)(17,18));