Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | SD16×#67 |
| Fitting | C22×C3×SD16 ⋊ C2 |
| Sylow | C3 ⋊ D4×SD16 |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(5,7);(2,3)(4,5)(6,7);(9,12)(10,15)(13,14);(8,9,11,14)(10,12,15,13)63 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×SD16, C2×SD16×#67, #11670476, … |
| maximal normal subgroup of | D3×D4×SD16, C2×SD16×#67, #11670476, … |
| maximal quotient of | #10784650, #10784655, #10784665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16441);