Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×C8×#67 |
| Fitting | C23×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5)(7,9);(4,5)(6,7)(8,9);(1,2)(10,11,12,14,13,15,16,17);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#806, #10685734, #10688078, … |
| maximal normal subgroup of | C8×#806, #10685734, #10688078, … |
| maximal quotient of | C2×C8×#213, C2×C8×#214, C2×C8×#215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16308);