Finite Group DatabasebetaFinite Group Databasebeta| order | 22100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×C17×D13 |
| unambiguous semidirect product | (D5×C13)⋊(C2×C5×C17) |
| unambiguous semidirect product | (C5×D13)⋊(C2×C5×C17) |
| unambiguous semidirect product | D65⋊(C2×C5×C17) |
| Fitting, socle, Hall | C52×C13×C17 ⋊ C22 |
| derived | C5×C13 ⋊ C22×C5×C17 |
| Hall | C52×C17 ⋊ C2×D13 |
| Hall | C52×C13 ⋊ C22×C17 |
| Hall | C13×C17 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×C17×D13 |
| Sylow | C13 ⋊ C2×C5×D5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | D5×D13 |
| commutator, cosocle, hypocenter | C5×C13 | C22×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C17 | C22 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C5×C17 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2210 |
2720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22100, 80);