Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#332 ⋊ C2 |
| Sylow | C3 ⋊ #1550 |
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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)(4,6,8,7)(5,9,10,11);(2,3)(4,5,8,10)(6,9,7,11)(12,14,17,13)(15,18,16,19);(5,9)(6,7)(10,11)(12,13,16,19,17,14,15,18)Polycyclic presentation:
2^7,3|a^2=e,b^2=g,c^2=f,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,d^b=dg,e^b=efg,h^b=h^2,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1550, C2×#68423, #10763542, … |
| maximal normal subgroup of | D3×#1550, C2×#68423, #10763542, … |
| maximal quotient of | #10683193, #10683251, #10683357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 999);