Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×D16 ⋊ C2 |
| Sylow | C3 ⋊ #2215 |
174 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 51 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)(5,7);(1,2,3)(8,9,14,20,11,15,18,21,12,16,22,23,17,19,10,13);(4,5)(6,7)(9,13)(10,14)(11,17)(15,23)(16,21)(18,22)(19,20)Polycyclic presentation:
2^7,3|b^2=df,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 | #10715824, #10715829, #10715834, … |
| maximal normal subgroup of | #10715824, #10715829, #10715834, … |
| maximal quotient of | #10709390, #10709441, #10709509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4045);