Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #73085 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #550 ⋊ D3 |
130 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 20 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) = 64 |
A minimal faithful permutation representation — 2 generators on 24 points:
(2,5)(3,8)(6,7)(9,23,18,16,19,24,13,14,20,10,11,22)(12,15,17,21);(1,2)(3,5)(4,7)(6,8)(11,17)(12,19)(14,21)(15,23)(18,20)(22,24)Polycyclic presentation:
2^4,3,2^3|b^2=h,c^2=d,f^2=h,g^2=h,b^a=bc,c^a=cd,e^a=e^2,f^a=gh,g^a=fh,c^b=cd,f^e=g,g^e=fgh,g^f=gh31 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73092, #11711972, #11711978, … |
| maximal normal subgroup of | C2×#73092, #11711972, #11711978, … |
| maximal quotient of | #11711053, #11711094, #11711119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5668);