Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #548⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #2971⋊C3 |
| Fitting, Sylow | #2971 ⋊ C3 |
117 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,3,5,4)(2,6,7,8)(9,10,13,16)(11,15,19,22,12,21,18,24,17,14,20,23);(1,2,4,6,5,7,3,8)(9,17,13,19)(10,21,16,23)(11,20,18,12)(14,24,22,15)Polycyclic presentation:
2^2,3,2^5|a^2=d,b^2=eh,d^2=e,f^2=h,g^2=h,b^a=be,f^c=g,g^c=fg,g^f=gh70 conjugacy classes — view the full character table.
| maximal subgroup of | #17654⋊C3, #17655⋊C3, #17688⋊C3, … |
| maximal normal subgroup of | #17654⋊C3, #17655⋊C3, #17688⋊C3, … |
| maximal quotient of | SL(2,𝔽3)×#97, #22530⋊C3, #22734⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5828);