Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×#100 |
| Fitting | C2×C3×#100 ⋊ C2 |
| Sylow | C3 ⋊ C22×#100 |
992 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 13 points:
(3,4,5)(7,10)(8,12);(6,7,8,11,9,10,12,13);(1,2)(4,5);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1390, #10710132, #10712663, … |
| maximal normal subgroup of | D3×#1390, #10710132, #10712663, … |
| maximal quotient of | C2×D3×#323, D3×#1460, C2×#68101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11271);