Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | SL(2,ℤ/4)⋊C8 |
163 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 163 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,4)(5,6,8)(9,10,11,13,12,14,15,16);(1,2,3,4)(6,7)Polycyclic presentation:
2^5,3,2^2|a^2=d,b^2=c,c^2=e,b^a=bd,f^a=f^2,g^a=h,h^a=g,g^f=h,h^f=gh56 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SL(2,ℤ/4)⋊C8, #11712672, #11712673, … |
| maximal normal subgroup of | C2×SL(2,ℤ/4)⋊C8, #11712672, #11712673, … |
| maximal quotient of | #11711080, #11711081, #11711083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5683);