Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | Dic3×#101 |
| Sylow | C3 ⋊ C4×#101 |
296 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 119 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 — 3 generators on 23 points:
(1,2,3)(8,10,12,18)(9,13,14,16)(11,19,20,17)(15,23,22,21);(8,9,11,15,12,14,20,22)(10,16,17,23,18,13,19,21);(2,3)(4,5,6,7)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10710364, Dic3×#355, #10710368, … |
| maximal normal subgroup of | #10710364, Dic3×#355, #10710368, … |
| maximal quotient of | Dic3×#324, #10685703, #10685707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2672);