Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #2897⋊C3 |
| Fitting, Sylow | #2897 ⋊ C3 |
193 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 36 points:
(5,6,8,12)(7,16,15,11)(9,26,21,25,20,28,19,14,22,13,10,27)(17,24,33,23,30,35,29,32,34,31,18,36);(1,2,3,4)(5,22,8,21)(6,36,12,35)(7,33,15,34)(9,10,19,20)(11,28,16,27)(13,24,25,32)(14,31,26,23)(17,30,29,18)Polycyclic presentation:
2^2,3,2^5|a^2=eh,b^2=h,d^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,d^b=dh,f^c=gh,g^c=fg,g^f=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#2897⋊C3, #60086⋊C3, #60087⋊C3, … |
| maximal normal subgroup of | C2×#2897⋊C3, #60086⋊C3, #60087⋊C3, … |
| maximal quotient of | #17438⋊C3, #17520⋊C3, #17550⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5813);