Finite Group DatabasebetaFinite Group Databasebeta| order | 22100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D17×D25 |
| unambiguous semidirect product | (C17×D25)⋊(C2×C13) |
| unambiguous semidirect product | (C25×D17)⋊(C2×C13) |
| unambiguous semidirect product | D425⋊(C2×C13) |
| Fitting, Hall | C13×C17×C25 ⋊ C22 |
| derived, Hall | C17×C25 ⋊ C22×C13 |
| Hall | C13×C25 ⋊ C2×D17 |
| Hall | C13×C17 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C13×D17 |
| Sylow | C17 ⋊ C2×C13×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D17×D25 |
| commutator, cosocle, hypocenter | C17×C25 | C22×C13 |
| Frattini | C5 | D5×C13×D17 |
| Fitting | C13×C17×C25 | C22 |
| socle | C5×C13×C17 | C2×D5 |
| LCS | G ▷ C17×C25 | |
| UCS | C1 ◁ C13 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5525 |
1820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22100, 34);