Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×D3×M16 |
| Fitting | C22×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C23×M16 |
1720 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 5 generators on 15 points:
(1,2)(3,4)(5,6,7)(9,12)(13,15);(8,9,10,13,11,12,14,15);(6,7);(3,4);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10700421, (C2×D3)⋊#338, #10700459, … |
| maximal normal subgroup of | #10700421, (C2×D3)⋊#338, #10700459, … |
| maximal quotient of | C22×D3×#97, C2×C4×D3×M16, C22×Dic3×M16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19728);