Finite Group DatabasebetaFinite Group Databasebeta| order | 23562 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3927 |
| unambiguous semidirect product | C7⋊(C3⋊D561) |
| unambiguous semidirect product | C11⋊(C3⋊D357) |
| unambiguous semidirect product | C17⋊(C3⋊D231) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C11×C17 | C2 |
| LCS | G ▷ C32×C7×C11×C17 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11781 |
Polycyclic presentation:
2,3^2,7,11,17|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^10,f^a=f^165892 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23562, 64);