Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#859 |
175 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 175 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 128 |
A minimal faithful permutation representation — 2 generators on 16 points:
(5,6,7,8)(9,15,16)(10,14,12);(1,2,3,4)(6,8)(10,13)(11,15)(14,16)Polycyclic presentation:
2^4,3,2^3|a^2=c,b^2=d,f^2=h,g^2=h,b^a=bd,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh46 conjugacy classes — view the full character table.
| maximal subgroup of | #11711053, #11711054, #11711055, … |
| maximal normal subgroup of | #11711053, #11711054, #11711055, … |
| maximal quotient of | C4⋊(SL(2,𝔽3)⋊C8), #11711070, #11711071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5636);