Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #2888⋊C3 |
| Fitting, Sylow | #2888 ⋊ C3 |
186 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 48 points:
(1,16,37,18,4,32,8,34,19,3,22,47)(2,24,40,15,10,39,11,29,25,9,26,42)(5,23,38,17,20,36,7,33,35,6,21,46)(12,44,45,13,27,48,14,31,41,30,28,43);(1,9,7,30,8,15,5,13)(2,6,14,18,11,17,12,3)(4,44,21,29,22,31,20,24)(10,34,28,33,26,16,27,23)(19,41,38,25,37,45,35,40)(32,43,36,39,47,48,46,42)Polycyclic presentation:
2^2,3,2^5|a^2=e,b^2=h,e^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,e^b=eh,f^c=fg,g^c=f,g^f=gh43 conjugacy classes — view the full character table.
| maximal subgroup of | #33371⋊C3, #33373⋊C3, C2×#2888⋊C3, … |
| maximal normal subgroup of | #33371⋊C3, #33373⋊C3, C2×#2888⋊C3, … |
| maximal quotient of | #17353⋊C3, #17419⋊C3, #17655⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5809);