Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×Q8×Dic3 |
| Sylow | C3 ⋊ C42×Q8 |
684 conjugacy classes of subgroups; only the 425 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 425 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 — 4 generators on 19 points:
(2,3)(8,9,10,11);(1,2,3)(12,14,15,19)(13,16,17,18);(12,13,15,17)(14,18,19,16);(4,5,6,7)120 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×Q8⋊C8, #10685796, #10685806, … |
| maximal normal subgroup of | Dic3×Q8⋊C8, #10685796, #10685806, … |
| maximal quotient of | C4×Dic3×C4⋊C4, C4×#4980, Dic3×#387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15025);