Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#4545 |
| Sylow | C3 ⋊ C2×#353 |
368 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 13 points:
(3,4,5)(7,10)(8,13)(11,12);(4,5)(6,7)(8,11,13,10)(9,12);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682926, #10682927, #10682950, … |
| maximal normal subgroup of | #10682926, #10682927, #10682950, … |
| maximal quotient of | C2×#67640, C2×#67635, #10704457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4346);