Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
| direct product | Dic3×#97 |
| Sylow | C3 ⋊ C4×#97 |
360 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(5,6,7,8)(10,13)(14,16)(17,18,19);(9,10,11,14,12,13,15,16);(1,2,3,4)(18,19)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10686100, Dic3×#329, #10686104, … |
| maximal normal subgroup of | #10686100, Dic3×#329, #10686104, … |
| maximal quotient of | Dic3×#322, C3⋊C8×#97, #10684539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2379);