Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#4528 |
| Sylow | C3 ⋊ C2×#324 |
328 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 125 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 — 3 generators on 21 points:
(3,4,5)(6,7,9,11)(8,10,12,13);(4,5)(7,10,11,13)(8,12)(14,15,16,18,17,19,20,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10682149, #10682150, #10682309, … |
| maximal normal subgroup of | #10682149, #10682150, #10682309, … |
| maximal quotient of | C2×#67638, #10683142, #10683176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4127);