Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×D3×SD16 |
| Fitting | C3×C4×SD16 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×SD16 |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(6,9)(7,12)(10,11)(13,14,15);(5,6,8,11)(7,9,12,10);(14,15);(1,2,3,4)84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C8×SD16, D3×SD16⋊C8, #10764647, … |
| maximal normal subgroup of | D3×C8×SD16, D3×SD16⋊C8, #10764647, … |
| maximal quotient of | D3×C8×SD16, D3×#1583, D3×#1582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12219);