Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#339 ⋊ C2 |
| Sylow | C3 ⋊ #1764 |
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 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 — 3 generators on 23 points:
(2,3)(8,10,12,19,13,20,11,18)(9,15,16,22,17,23,14,21);(1,2,3)(4,5,6,7)(9,14,17,16)(15,21,23,22);(8,9,12,16,13,17,11,14)(10,15,19,22,20,23,18,21)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1764, C2×#68739, #10793030, … |
| maximal normal subgroup of | D3×#1764, C2×#68739, #10793030, … |
| maximal quotient of | #10685858, #10685868, #10685875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1315);