Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×D3×#41 |
| Fitting | C3×C4×#41 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×#41 |
1728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 5 generators on 15 points:
(5,7,8,11)(6,10,9,12)(13,14,15);(6,9)(10,12);(5,6)(7,10)(8,9)(11,12);(14,15);(1,2,3,4)120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1476, D3×#1477, #10761558, … |
| maximal normal subgroup of | D3×#1476, D3×#1477, #10761558, … |
| maximal quotient of | C4×D3×#117, C42×D3×D4, C42×D3×Q8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18409);