Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | Dic3×#104 |
| Sylow | C3 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(5,7)(6,9)(8,10)(11,12)(13,14,15);(5,6,8,11,9,7,12,10);(1,2,3,4)(14,15)84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#104, C2×Dic3×#104, #10792909, … |
| maximal normal subgroup of | C4×D3×#104, C2×Dic3×#104, #10792909, … |
| maximal quotient of | Dic3×D4⋊C8, Dic3×Q8⋊C8, #10685801, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2929);