Finite Group DatabasebetaFinite Group Databasebeta| order | 22100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D221⋊D25 |
| unambiguous semidirect product | D325⋊D17 |
| unambiguous semidirect product | D425⋊D13 |
| Fitting, derived, Hall | C13×C17×C25 ⋊ C22 |
| Hall | C17×C25 ⋊ C2×D13 |
| Hall | C13×C25 ⋊ C2×D17 |
| Hall | C13×C17 ⋊ C2×D25 |
| Sylow | C25 ⋊ D13×D17 |
| Sylow | C17 ⋊ D13×D25 |
| Sylow | C13 ⋊ D17×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C13×C17×C25 | C22 |
| Frattini | C5 | D65⋊D17 |
| socle | C5×C13×C17 | C2×D5 |
| LCS | G ▷ C13×C17×C25 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5525 |
Polycyclic presentation:
2^2,5,13,17,5|c^5=f^4,d^a=d^12,e^a=e^16,c^b=c^4f,d^b=d^12,f^b=f^41424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22100, 44);