Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×C4⋊#1020 |
| Fitting | C24×C42 ⋊ D3 |
5598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 5598 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,3,4)(5,7,6)(9,11,12,10);(1,4,3,2)(7,8)(14,16);(9,10,12,11)(13,14,15,16)112 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11713271, C4×#11713272, C4×D4×#1020 |
| maximal normal subgroup of | C4×#11713271, C4×#11713272, C4×D4×#1020 |
| maximal quotient of | #72341790, #72341899 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,3,4)(5,7,6)(9,11,12,10), (1,4,3,2)(7,8)(14,16), (9,10,12,11)(13,14,15,16));