Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#330 ⋊ C2 |
| Sylow | C3 ⋊ #1526 |
226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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)(4,6,8,7)(5,9,10,11)(12,15,17,16)(13,18,14,19);(1,2,3)(4,5)(6,9)(7,11)(8,10)(12,14,17,13)(15,19,16,18);(5,9,10,11)(12,13,16,19,17,14,15,18)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=g,d^2=g,e^2=f,b^a=bd,d^a=df,d^b=dg,e^b=efg,h^c=h^257 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1526, C2×#68362, #10763082, … |
| maximal normal subgroup of | D3×#1526, C2×#68362, #10763082, … |
| maximal quotient of | #10683140, #10683163, #10683432, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 938);