Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C24 |
| direct product | C2×(C2×D3)⋊C16 |
| Fitting | C22×C3×C16 ⋊ C2 |
| Sylow | C3 ⋊ C2×C22⋊C16 |
272 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 25 points:
(3,4,5)(7,9)(10,11,12,15,13,16,18,21,14,17,19,22,20,23,24,25);(4,5)(6,7)(8,9);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | #10682525, #10710213, C4×(C2×D3)⋊C16, … |
| maximal normal subgroup of | #10682525, #10710213, C4×(C2×D3)⋊C16, … |
| maximal quotient of | C2×#67522, C2×#67524, #10704383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3984);