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 ⋊ #261 |
| Hall | C13×C25 ⋊ #595 |
| Hall | C13×C17 ⋊ Dic25 |
| Sylow | C25 ⋊ #11725131 |
| Sylow | C17 ⋊ #13049904 |
| Sylow | C13 ⋊ #13133320 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C17×C25 | C4 |
| Frattini | C5 | #17984471 |
| socle | C5×C13×C17 | Dic5 |
| prime radical | C5×D221 | D5 |
| cosocle | C25×D221 | 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^4,c^a=c^4f,d^a=d^5,e^a=e^4,f^a=f^4,d^b=d^12,e^b=e^161403 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22100, 37);