Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#953 |
| Fitting | C24×C3×C4 ⋊ C2 |
| Sylow | C3 ⋊ C4×#120 |
1224 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1224 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) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(9,11);(13,15);(2,3)(8,9)(10,11)(12,13)(14,15);(4,5,6,7)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10689869, #10689879, #10800679, … |
| maximal normal subgroup of | #10689869, #10689879, #10800679, … |
| maximal quotient of | C4×#5213, C4×#5210, C4×#5247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16606);