Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×C4⋊Dic3 |
| Sylow | C3 ⋊ C2×C4×C4⋊C4 |
928 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5)(10,11,12,13);(4,5)(6,7,8,9)(11,13);(1,2)(14,15,16,17);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#67704, C2×#67655, #10684722, … |
| maximal normal subgroup of | C2×#67704, C2×#67655, #10684722, … |
| maximal quotient of | C2×C4×C3⋊#95, C42×C4⋊Dic3, C2×#71534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14631);