Finite Group DatabasebetaFinite Group Databasebeta| order | 22156 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×Dic191 |
| unambiguous semidirect product | C191⋊(C4×C29) |
| derived, Sylow | C191 ⋊ C4×C29 |
| Hall | C29×C191 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D191 |
| commutator, hypocenter | C191 | C4×C29 |
| Frattini | C2 | C29×D191 |
| Fitting, socle, prime radical | C2×C29×C191 | C2 |
| cosocle | C2×C191 | C2×C29 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C2×C29 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22156 |
5626 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22156, 3);