Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | D3×#339 |
| Fitting | C3×#339 ⋊ C2 |
| Sylow | C3 ⋊ C2×#339 |
488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 15 points:
(6,9,11,10)(13,14,15);(1,2,3,4)(5,6)(7,9)(8,11)(10,12);(14,15)84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#339, D3×#1733, #10792576, … |
| maximal normal subgroup of | C2×D3×#339, D3×#1733, #10792576, … |
| maximal quotient of | D3×#1276, #10684627, #10684633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1328);