Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C3 ⋊ #1715 |
220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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:
(2,3)(5,10)(8,11)(12,13,14,16,15,17,18,19);(1,2,3)(4,5,9,11,7,10,6,8);(5,8)(6,9)(10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|b^2=df,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10683052, #10683054, #10708956, … |
| maximal normal subgroup of | #10683052, #10683054, #10708956, … |
| maximal quotient of | #10688973, #10694963, #10694977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3853);