Finite Group DatabasebetaFinite Group Databasebeta| order | 22100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C13×C17×C25 ⋊ C4 |
| Hall | C17×C25 ⋊ Dic13 |
| Hall | C13×C25 ⋊ Dic17 |
| Hall | C13×C17 ⋊ #1035 |
| Sylow | C25 ⋊ Dic221 |
| Sylow | C17 ⋊ #13049906 |
| Sylow | C13 ⋊ #13133322 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C17×C25 | C4 |
| Frattini | C5 | #17984466 |
| socle | C5×C13×C17 | AGL(1,𝔽5) |
| prime radical, cosocle | C13×C17×D25 | C2 |
| LCS | G ▷ C13×C17×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5525 |
Polycyclic presentation:
2^2,5,13,17,5|a^2=b,c^5=f,c^a=c^2f,d^a=d^12,e^a=e^16,f^a=f^2,c^b=c^4f^4,f^b=f^41550 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22100, 32);