Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4539 |
| Sylow | C3 ⋊ C2×#352 |
278 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(6,8,10,16)(7,11,14,20)(9,15,18,17)(12,19,21,13);(4,5)(6,7,8,12)(9,13,17,20)(10,14,16,21)(11,18,19,15);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4539, Dic3×#352, #10710329, … |
| maximal normal subgroup of | C4×#4539, Dic3×#352, #10710329, … |
| maximal quotient of | C2×#67627, C2×#67636, #10704442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4279);