Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#344 ⋊ C2 |
| Sylow | C3 ⋊ #1829 |
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6)(5,10,9,12)(7,14)(8,13)(11,18,16,19)(15,17);(2,3)(5,9)(7,15)(10,12)(14,17);(4,5,7,11,8,9,15,16)(6,12,14,19,13,10,17,18)Polycyclic presentation:
2^7,3|a^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^2,e^c=eg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1829, C2×#69026, #10795057, … |
| maximal normal subgroup of | D3×#1829, C2×#69026, #10795057, … |
| maximal quotient of | #10688645, #10688651, #10688702, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1602);