Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D3×#447 |
| Fitting | C3×#447 ⋊ C2 |
| Sylow | C3 ⋊ C2×#447 |
1048 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 155 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) = 48 |
A minimal faithful permutation representation — 4 generators on 15 points:
(2,4)(13,14,15);(6,9)(7,12)(10,11);(1,2)(3,4)(5,6)(7,9)(8,11)(10,12);(14,15)57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1595, D3×#1597, D3×#1598, … |
| maximal normal subgroup of | D3×#1595, D3×#1597, D3×#1598, … |
| maximal quotient of | D3×#1595, D3×#1607, D3×#1598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12576);