Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C19 ⋊ C2 |
| Sylow | C19 ⋊ #2312 |
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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=g,b^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^18404 conjugacy classes — view the full character table.
| maximal subgroup of | #18076003, #18079991, #18079993, … |
| maximal normal subgroup of | #18076003, #18079991, #18079993, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 7105);