Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C19 ⋊ C8×C22⋊C4 |
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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,e^2=g,b^a=bd,h^a=h^18,h^b=h^18,h^c=h^18440 conjugacy classes — view the full character table.
| maximal subgroup of | #18073079, #18073083, #18073091, … |
| maximal normal subgroup of | #18073079, #18073083, #18073091, … |
| maximal quotient of | C22⋊C8×C19⋊C8, #18073015, #18073032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 4284);