Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #2912⋊C3 |
| Fitting, Sylow | #2912 ⋊ C3 |
131 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 36 points:
(5,6,7,11,8,12,15,22)(9,14,31,23,19,28,29,34,20,13,17,35,18,26,32,33,10,27,16,24,21,25,30,36);(1,2,3,4)(5,20,8,21)(6,35,12,36)(7,32,15,31)(9,19,18,10)(11,27,22,28)(13,34,25,24)(14,23,26,33)(16,17,29,30)Polycyclic presentation:
2^2,3,2^5|a^2=eh,b^2=d,d^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,f^c=g,g^c=fg,g^f=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | #33388⋊C3, #33404⋊C3, C2×#2912⋊C3, … |
| maximal normal subgroup of | #33388⋊C3, #33404⋊C3, C2×#2912⋊C3, … |
| maximal quotient of | #17788⋊C3, #17835⋊C3, #20348⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5821);