Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#4526 |
| Sylow | C3 ⋊ C2×#342 |
680 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 17 points:
(3,4,5)(6,7,8,9)(10,11)(12,14)(13,15)(16,17);(4,5)(11,14,15,17)(12,16);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10682306, #10682308, Dic3×#342, … |
| maximal normal subgroup of | #10682306, #10682308, Dic3×#342, … |
| maximal quotient of | C2×#67613, #10684781, #10684787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4116);