Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×M16 ⋊ D3 |
265 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4)(5,8,9,16,10,17,7,14)(6,12,11,15,13,20,18,19);(5,7,10,9)(6,11,13,18)(8,16,17,14)(12,19,20,15);(2,3)(5,6)(7,11)(8,15)(9,18)(10,13)(12,16)(14,20)(17,19)Polycyclic presentation:
2^5,3,2^2|b^2=e,c^2=d,d^2=e,c^a=cd,d^a=de,f^a=f^2,g^a=h,h^a=g,c^b=ce,g^f=h,h^f=gh32 conjugacy classes — view the full character table.
| maximal subgroup of | #11713367, #11713369, #11713419, … |
| maximal normal subgroup of | #11713367, #11713369, #11713419, … |
| maximal quotient of | #11712178, #11712180, #11712182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18020);