Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×D3×SD16 |
| Fitting | C22×C3×SD16 ⋊ C2 |
| Sylow | C3 ⋊ C23×SD16 |
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 5 generators on 15 points:
(1,2)(3,4)(5,6,7)(9,12)(10,15)(13,14);(1,2)(3,4)(8,9,11,14)(10,12,15,13);(6,7);(3,4);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1877, D3×#1880, #10796614, … |
| maximal normal subgroup of | D3×#1877, D3×#1880, #10796614, … |
| maximal quotient of | C22×D3×#102, C22×D3×#103, C22×D3×#106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19749);