Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#4936 |
| Sylow | C3 ⋊ C2×#382 |
712 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 389 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) = 384 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,8,9,7)(14,16,17,20)(15,19,18,21);(6,7,9,8)(14,15)(16,19)(17,18)(20,21);(4,5)(7,8)(10,11,12,13)(15,18)(19,21);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10684802, #10684804, C2×#67738, … |
| maximal normal subgroup of | #10684802, #10684804, C2×#67738, … |
| maximal quotient of | C2×#71534, C2×#71535, C4×#4936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14634);