Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#470 |
| Fitting | C3×#470 ⋊ C2 |
| Sylow | C3 ⋊ C2×#470 |
492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(2,4)(7,15)(10,19)(13,20)(16,18)(21,22,23);(5,7,14,18,9,15,8,16)(6,10,17,20,12,19,11,13);(1,2)(3,4)(5,6,9,12)(7,13,15,20)(8,17,14,11)(10,18,19,16);(22,23)48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1340, D3×#1342, D3×#2191, … |
| maximal normal subgroup of | D3×#1340, D3×#1342, D3×#2191, … |
| maximal quotient of | D3×#1689, D3×#1695, D3×#1703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13478);