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 | C42×#67 |
| Fitting | C22×C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ C42×D4 |
924 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 381 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(13,15);(2,3)(12,13)(14,15);(8,9,10,11);(4,5,6,7)144 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#67⋊C8, C4×C8×#67, C4×#4730, … |
| maximal normal subgroup of | C4×#67⋊C8, C4×C8×#67, C4×#4730, … |
| maximal quotient of | C42×#217, C42×(C2×D3)⋊C4, C42×Dic3⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14633);