Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
191 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 30 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 — 2 generators on 20 points:
(1,2,4)(5,7,9,15)(6,10,12,13)(8,16,17,14)(11,19,20,18);(2,3)(5,6,8,11,9,12,17,20)(7,13,14,19,15,10,16,18)Polycyclic presentation:
2^5,3,2^2|a^2=c,b^2=e,c^2=e,b^a=bd,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 | #11711506, #11711507, #11711616, … |
| maximal normal subgroup of | #11711506, #11711507, #11711616, … |
| maximal quotient of | #11711010, #11711022, #11711024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5722);