Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×#874 |
| Fitting | C3×C43 ⋊ C2 |
| Sylow | C3 ⋊ C4×#127 |
924 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 277 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)(12,13,14,15);(8,9,10,11);(2,3)(9,11)(13,15);(4,5,6,7)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10683161, #10683242, #10683244, … |
| maximal normal subgroup of | #10683161, #10683242, #10683244, … |
| maximal quotient of | C4×#4939, C4×#4935, C4×#4671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5881);