Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4×C8×C19 ⋊ C2 |
| Sylow | C19 ⋊ #1750 |
336 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^7,19|a^2=e,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=cg,h^a=h^18632 conjugacy classes — view the full character table.
| maximal subgroup of | #18074061, #18074066 |
| maximal normal subgroup of | #18074061, #18074066 |
| maximal quotient of | #18073029, #18073036, #18073058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 4277);