Finite Group DatabasebetaFinite Group Databasebeta| order | 22592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C353 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D353 |
| commutator | C22×C353 | C22×C4 |
| Fitting, prime radical | C25×C353 | C2 |
| socle, cosocle | C23×C353 | C23 |
| hypercenter | C25 | D353 |
| hypocenter | C353 | #379 |
| LCS | G ▷ C22×C353 ▷ C353 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5648 |
Polycyclic presentation:
2^6,353|a^2=f,b^a=bd,c^a=ce,g^a=g^3525660 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22592, 405);