Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4949 |
| Sylow | C3 ⋊ C2×#399 |
908 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 261 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) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,7)(8,9)(11,13)(14,16)(15,18)(17,20)(19,21);(10,11,12,13)(16,20)(18,21);(1,2)(4,5)(7,9)(11,13)(14,15,17,19)(16,18,20,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10690214, #10690216, #10690229, … |
| maximal normal subgroup of | #10690214, #10690216, #10690229, … |
| maximal quotient of | C2×#71547, C2×#71546, C2×#69420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14681);