Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×C4⋊C8 |
| Fitting | C2×C3×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ C22×C4⋊C8 |
640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(6,7,8,9);(7,9)(10,11,12,14,13,15,16,17);(1,2)(4,5);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1277, #10684647, #10684661, … |
| maximal normal subgroup of | D3×#1277, #10684647, #10684661, … |
| maximal quotient of | C2×D3×#334, C2×D3×#335, D3×#1564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11585);