Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#5406 |
| Fitting | C2×#131 ⋊ D3 |
257 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 257 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 34 points:
(3,10,29,9,18,26,13,33,17,4,14,32,8,25,30,22,6,24,5,20,19,12,27,34)(7,11,15,21,16,23,28,31);(4,9)(5,13)(6,7)(10,21)(11,20)(12,22)(14,28)(15,27)(16,18)(17,19)(23,33)(24,34)(25,31)(26,32);(1,2)40 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#5406, #11712868, #11713138, … |
| maximal normal subgroup of | C4×#5406, #11712868, #11713138, … |
| maximal quotient of | C2×#73021, C2×#73012, C2×#73024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18025);