Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×#101 |
| Fitting | C2×C3×#101 ⋊ C2 |
| Sylow | C3 ⋊ C22×#101 |
736 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,8,10,16)(7,11,12,14)(9,17,18,15)(13,21,20,19);(6,7,9,13,10,12,18,20)(8,14,15,21,16,11,17,19);(1,2)(4,5);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1394, #10710170, #10712723, … |
| maximal normal subgroup of | D3×#1394, #10710170, #10712723, … |
| maximal quotient of | C2×D3×#324, D3×#1461, C2×#68125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11280);