Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | D3×C8×Q8 |
| Fitting | C3×C8×Q8 ⋊ C2 |
| Sylow | C3 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 241 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(9,11,12,16)(10,13,14,15)(17,18,19);(9,10,12,14)(11,15,16,13);(18,19);(1,2,3,5,4,6,7,8)120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×Q8⋊C16, #10704992, #10705128, … |
| maximal normal subgroup of | D3×Q8⋊C16, #10704992, #10705128, … |
| maximal quotient of | D3×C8×C4⋊C4, C8×#887, C8×Q8×Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12492);