Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C19 ⋊ #1444 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D19 |
| commutator | C23×C19 | C22×C4 |
| Fitting | C2×C19×#95 | C2 |
| socle, prime radical, cosocle | C24×C19 | C23 |
| hypercenter | C2×#95 | D19 |
| hypocenter | C19 | #1444 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
608 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2432 |
Polycyclic presentation:
2^7,19|a^2=g,b^2=d,c^2=e,b^a=bd,c^a=ce,h^a=h^18,c^b=cf404 conjugacy classes — view the full character table.
| maximal subgroup of | #18076588, #18076589, #18076602, … |
| maximal normal subgroup of | #18076588, #18076589, #18076602, … |
| maximal quotient of | #18070467, #18091143, #18091147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 2775);