Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×#926 |
| Sylow | C3 ⋊ C4×#117 |
752 conjugacy classes of subgroups; only the 421 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 421 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) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(13,17)(16,19);(12,14,15,18)(13,16,17,19);(2,3)(8,9,10,11)(12,13)(14,16)(15,17)(18,19);(4,5,6,7)144 conjugacy classes — view the full character table.
| maximal subgroup of | #10684585, #10684591, #10684625, … |
| maximal normal subgroup of | #10684585, #10684591, #10684625, … |
| maximal quotient of | C4×#4932, C42×#217, C42×C4⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14632);