Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#5400 |
| Fitting | C23×C8 ⋊ D3 |
301 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 301 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(3,4,6)(7,8,9,12,10,11,13,14);(4,5)(8,11)(12,14);(1,2)56 conjugacy classes — view the full character table.
| maximal subgroup of | #11711563, #11712569, C4×#5400, … |
| maximal normal subgroup of | #11711563, #11712569, C4×#5400, … |
| maximal quotient of | C2×#73018, C2×#73010, #11711842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18012);