Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C3×SD32 ⋊ C2 |
| Sylow | C3 ⋊ #2248 |
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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 — 3 generators on 23 points:
(2,3)(4,5,6,7);(1,2,3)(8,9,14,23,11,15,10,13,12,16,17,21,18,20,19,22);(5,7)(9,13)(10,17)(11,18)(14,19)(15,23)(16,22)(20,21)Polycyclic presentation:
2^7,3|b^2=dfg,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2248, C2×#71479, #10950589, … |
| maximal normal subgroup of | D3×#2248, C2×#71479, #10950589, … |
| maximal quotient of | #10709847, #10709849, #10709851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4055);