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 | #2984⋊C3 |
| Fitting, Sylow | #2984 ⋊ C3 |
119 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 2 generators on 24 points:
(2,5)(6,8)(10,14)(11,17,12)(15,24,16,21,23,22)(18,19,20);(1,2,3,6,4,5,7,8)(9,24,13,23)(10,19,14,17)(11,16,18,22)(12,21,20,15)Polycyclic presentation:
2^2,3,2^5|a^2=d,d^2=e,f^2=h,g^2=h,b^a=beh,f^c=fg,g^c=f,g^f=gh70 conjugacy classes — view the full character table.
| maximal subgroup of | #17425⋊C3, #17430⋊C3, #17549⋊C3, … |
| maximal normal subgroup of | #17425⋊C3, #17430⋊C3, #17549⋊C3, … |
| maximal quotient of | #20572⋊C3, SL(2,𝔽3)×C22⋊C8, #22734⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5830);