Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #2913⋊C3 |
| Fitting, Sylow | #2913 ⋊ 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:
(5,6,12,22,8,13,7,11)(9,28,32,33,10,30,16,34,20,14,17,36,18,15,31,23,19,29,25,24,21,27,26,35);(1,2,3,4)(5,21,8,20)(6,36,13,35)(7,31,12,32)(9,10,18,19)(11,30,22,29)(14,24,27,34)(15,33,28,23)(16,26,25,17)Polycyclic presentation:
2^2,3,2^5|a^2=eh,b^2=dh,d^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,f^c=gh,g^c=fgh,g^f=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | #33381⋊C3, #33382⋊C3, #33410⋊C3, … |
| maximal normal subgroup of | #33381⋊C3, #33382⋊C3, #33410⋊C3, … |
| maximal quotient of | #17789⋊C3, #17837⋊C3, #20348⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5822);