Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C19 ⋊ #3502 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D19 |
| commutator, socle, cosocle | C22×C19 | C25 |
| Fitting | C2×C4×Q8×C19 | C2 |
| prime radical | C23×C19 | C24 |
| hypercenter | C2×C4×Q8 | D19 |
| hypocenter | C19 | #3502 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C2×C4×Q8 | |
964 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 964 conjugacy classes of subgroups — too many to draw. Only its 553 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=g,b^2=f,c^2=g,d^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^18,d^b=df404 conjugacy classes — view the full character table.
| maximal subgroup of | #18074101, #18074104, #18074538, … |
| maximal normal subgroup of | #18074101, #18074104, #18074538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 18320);