Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#4473 |
| Sylow | C3 ⋊ C2×#354 |
284 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 69 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)(7,11,12,19)(8,15,16,17)(9,18)(13,21,20,14);(4,5)(6,7,10,14)(8,11,16,13)(9,12,18,21)(15,19,17,20);(1,2)48 conjugacy classes — view the full character table.
| maximal subgroup of | #10710352, C4×#4473, #10710356, … |
| maximal normal subgroup of | #10710352, C4×#4473, #10710356, … |
| maximal quotient of | C2×#67455, C2×#67452, #10704463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2593);