Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1767 |
292 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,7,5)(13,16)(17,19);(9,11)(12,13,14,17,15,16,18,19);(2,3)(4,5,7,6)(8,9,10,11)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=de,f^2=g,b^a=bd,h^a=h^2,c^b=cg96 conjugacy classes — view the full character table.
| maximal subgroup of | #10687948, #10687949, #10687952, … |
| maximal normal subgroup of | #10687948, #10687949, #10687952, … |
| maximal quotient of | #10686317, #10686328, #10686350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2385);