Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #2901⋊C3 |
| Fitting, Sylow | #2901 ⋊ C3 |
188 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 188 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) = 32 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,2,6,12)(3,9,7,8)(4,11,15,26,5,27,16,28,17,10,18,25)(13,24,29,21,14,31,19,22,30,23,20,32);(1,25,3,32,6,27,7,31)(2,30,9,15,12,29,8,17)(4,28,13,22,16,11,19,24)(5,10,14,23,18,26,20,21)Polycyclic presentation:
2^2,3,2^5|a^2=eh,b^2=h,d^2=h,e^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,d^b=dh,f^c=g,g^c=fgh,g^f=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#2901⋊C3, #60093⋊C3, #60183⋊C3, … |
| maximal normal subgroup of | C2×#2901⋊C3, #60093⋊C3, #60183⋊C3, … |
| maximal quotient of | #17438⋊C3, #17439⋊C3, #17507⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5816);