Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D3×#494 |
| Fitting | C3×#494 ⋊ C2 |
| Sylow | C3 ⋊ C2×#494 |
552 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 165 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) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3,4)(21,22,23);(5,7,14,18,9,16,8,15)(6,10,17,20,12,19,11,13);(2,4)(5,6,9,12)(7,13,16,20)(8,17,14,11)(10,18,19,15);(22,23)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1358, D3×#1362, #10706443, … |
| maximal normal subgroup of | D3×#1358, D3×#1362, #10706443, … |
| maximal quotient of | D3×#1707, D3×#1710, D3×#1713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14374);