Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
208 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 208 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) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 24 points:
(3,7)(5,8)(9,15,21,10,19,23,12,17,22,11,13,24)(14,18,20,16);(1,3,4,7)(2,5,6,8);(1,2,4,6)(3,5,7,8)(9,10,12,11)(13,18,19,16)(14,17,20,15)(21,24,22,23)Polycyclic presentation:
2^4,3,2^3|a^2=d,b^2=dh,c^2=h,f^2=h,g^2=h,e^a=e^2,f^a=gh,g^a=fh,c^b=cdh,f^e=g,g^e=fgh,g^f=gh40 conjugacy classes — view the full character table.
| maximal subgroup of | #11712290, #11712291, #11712298, … |
| maximal normal subgroup of | #11712290, #11712291, #11712298, … |
| maximal quotient of | #11712905, #11712992, #11713043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17979);