Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | Dic3×H(5,𝔽2) |
| Sylow | C3 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 1063 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 — 5 generators on 15 points:
(6,10)(9,11)(13,14,15);(7,12)(9,11);(5,7)(6,9)(8,12)(10,11);(5,6)(7,11)(8,10)(9,12);(1,2,3,4)(14,15)102 conjugacy classes — view the full character table.
| maximal subgroup of | #10801056, Dic3×#453, #10801067, … |
| maximal normal subgroup of | #10801056, Dic3×#453, #10801067, … |
| maximal quotient of | Dic3×#518, Dic3×#520, Dic3×#534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19855);