Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#823 |
| Fitting | C3×C4×M16 ⋊ C2 |
| Sylow | C3 ⋊ C4×#100 |
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 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) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(8,9,10,13,11,12,14,15);(2,3)(9,12)(10,14);(4,5,6,7)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10685744, C8×#823, #10685754, … |
| maximal normal subgroup of | #10685744, C8×#823, #10685754, … |
| maximal quotient of | C4×#4468, #10685698, #10685711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2445);