Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#825 |
| Fitting | C22×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C22×#104 |
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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:
(5,6,7)(8,10,11,14,12,13,15,9);(6,7)(8,9)(10,11)(12,14)(13,15);(3,4);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10700696, #10700698, #10700703, … |
| maximal normal subgroup of | #10700696, #10700698, #10700703, … |
| maximal quotient of | C22×#4483, C22×#4484, C2×#70754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16353);