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 | #2991⋊C3 |
| Fitting, Sylow | #2991 ⋊ C3 |
114 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)(9,10,11,14)(12,23,13,21,19,22,17,24,18,15,20,16);(1,2,4,6,5,7,3,8)(9,19,11,20)(10,24,14,23)(12,18,17,13)(15,16,21,22)Polycyclic presentation:
2^2,3,2^5|a^2=dh,b^2=eh,d^2=e,f^2=h,g^2=h,b^a=beh,f^c=fg,g^c=fh,g^f=gh70 conjugacy classes — view the full character table.
| maximal subgroup of | #17518⋊C3, #17520⋊C3, #17773⋊C3, … |
| maximal normal subgroup of | #17518⋊C3, #17520⋊C3, #17773⋊C3, … |
| maximal quotient of | #20572⋊C3, #22530⋊C3, SL(2,𝔽3)×C4⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5832);