Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1997 |
260 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 101 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,7,11)(5,8,9,10);(12,14,16,18,17,19,15,13);(2,3)(4,5,7,9)(6,10,11,8)(12,13,16,19,17,18,15,14)Polycyclic presentation:
2^7,3|a^2=f,b^2=deg,c^2=ef,e^2=g,f^2=g,b^a=bd,c^a=cef,d^a=dg,h^a=h^2,d^b=dg,e^b=eg,f^b=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10687406, #10687412, #10687413, … |
| maximal normal subgroup of | #10687406, #10687412, #10687413, … |
| maximal quotient of | #10695226, #10695230, #10695244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2455);