Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×M16×C19 ⋊ C2 |
| Sylow | C19 ⋊ #1759 |
320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 320 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.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^7,19|a^2=e,b^2=f,c^2=e,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^18,c^b=cg,h^b=h^18404 conjugacy classes — view the full character table.
| maximal subgroup of | #18074394, #18074396, #18074401, … |
| maximal normal subgroup of | #18074394, #18074396, #18074401, … |
| maximal quotient of | #18073144, #18073149, #18073164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 4323);