Finite Group DatabasebetaFinite Group Databasebeta| order | 22436 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×Dic79 |
| unambiguous semidirect product | C79⋊(C4×C71) |
| derived, Sylow | C79 ⋊ C4×C71 |
| Hall | C71×C79 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C71 | D79 |
| commutator, hypocenter | C79 | C4×C71 |
| Frattini | C2 | C71×D79 |
| Fitting, socle, prime radical | C2×C71×C79 | C2 |
| cosocle | C2×C79 | C2×C71 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C2×C71 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22436 |
5822 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22436, 3);