Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | Dic3×#131 |
| Sylow | C3 ⋊ C4×#131 |
572 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 377 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(7,13)(10,16)(14,19)(17,20)(21,22,23);(5,7)(6,10)(8,14)(9,13)(11,17)(12,16)(15,19)(18,20);(5,6,8,11,9,12,15,18)(7,10,14,17,13,16,19,20);(1,2,3,4)(22,23)120 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#350, #10710242, #10711122, … |
| maximal normal subgroup of | Dic3×#350, #10710242, #10711122, … |
| maximal quotient of | C3⋊C8×#131, C8×#948, #10760797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16357);