Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26 |
| direct product | C22×#815 |
| Sylow | C3 ⋊ C22×#97 |
680 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 469 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:
(5,6,7)(12,13,14,17,15,16,18,19);(6,7)(8,9,10,11)(13,16)(17,19);(3,4);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | #10700335, #10700338, #10700345, … |
| maximal normal subgroup of | #10700335, #10700338, #10700345, … |
| maximal quotient of | C22×#4455, C22×#4454, C2×#69725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16301);