Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | D3×C8×D4 |
| Fitting | C3×C8×D4 ⋊ C2 |
| Sylow | C3 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(2,4)(13,14,15);(1,2)(3,4);(14,15);(5,6,7,9,8,10,11,12)120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4⋊C16, #10704892, #10705096, … |
| maximal normal subgroup of | D3×D4⋊C16, #10704892, #10705096, … |
| maximal quotient of | D3×C8×D8, D3×C8×SD16, D3×C8×Q16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11996);