Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1459 |
332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,8,7)(5,9,11,10);(12,14)(13,16)(15,19)(17,18);(2,3)(4,5,7,10,8,11,6,9)(12,13)(14,18,19,16)(15,17)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,e^2=g,b^a=bd,d^a=df,h^a=h^2,e^b=ef84 conjugacy classes — view the full character table.
| maximal subgroup of | #10682182, #10682183, #10682188, … |
| maximal normal subgroup of | #10682182, #10682183, #10682188, … |
| maximal quotient of | #10683146, #10683151, #10683219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4176);