Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | SD16×S4 |
| Fitting | C22×SD16 ⋊ D3 |
298 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 12 points:
(1,2,4,3);(2,3,4)(6,9)(7,12)(10,11);(5,6,8,11)(7,9,12,10)35 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16×S4, S4×#135, #11714904, … |
| maximal normal subgroup of | C2×SD16×S4, S4×#135, #11714904, … |
| maximal quotient of | #11712276, #11712277, #11712278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18035);