Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#4532 |
| Sylow | C3 ⋊ C2×#339 |
488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 17 points:
(3,4,5)(6,7,8,9)(10,11)(12,14)(13,16)(15,17);(4,5)(10,11,12,14,13,16,17,15);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#339, C4×#4532, #10700362, … |
| maximal normal subgroup of | Dic3×#339, C4×#4532, #10700362, … |
| maximal quotient of | C2×#67736, #10684628, #10684634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4149);