Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4451 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4486 |
| Sylow | C3 ⋊ C2×#332 |
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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 — 3 generators on 21 points:
(3,4,5)(7,10)(8,13)(11,12)(14,15,16,18,17,19,20,21);(4,5)(6,7,9,12)(8,10,13,11)(15,18)(16,20)(19,21);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10686134, C4×#4486, #10686147, … |
| maximal normal subgroup of | #10686134, C4×#4486, #10686147, … |
| maximal quotient of | C2×#67477, #10683164, #10683466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3010);