Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
302 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 302 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)(6,11)(7,14)(8,16)(10,17)(12,13)(18,19);(5,7)(6,10)(8,15)(9,14)(11,19)(12,17)(13,18)(16,20);(2,3)(5,6,9,13)(7,10,14,18)(8,11,16,12)(15,19,20,17)Polycyclic presentation:
2^5,3,2^2|a^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^2,g^a=h,h^a=g,c^b=ce,d^c=de,g^f=h,h^f=gh32 conjugacy classes — view the full character table.
| maximal subgroup of | #11713355, #11713357, #11713419, … |
| maximal normal subgroup of | #11713355, #11713357, #11713419, … |
| maximal quotient of | #11711989, #11711992, #11711997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18088);