Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #226⋊C8 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,5,4,6,7,8)(9,19,21)(10,15,24,14,20,23)(11,18,13)(16,17);(9,10,13,14)(11,17,19,16)(12,20,22,15)(18,24,21,23)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^2=c,c^2=d,f^2=h,g^2=h,b^a=bh,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#226⋊C8, #11711829, C8×#983, … |
| maximal normal subgroup of | C2×#226⋊C8, #11711829, C8×#983, … |
| maximal quotient of | #11711000, #11711087, #11711106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5584);