Finite Group DatabasebetaFinite Group Databasebeta| order | 17908 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C11⋊D11)⋊D37 |
| unambiguous semidirect product | D407⋊D11 |
| Fitting, socle, derived, Hall | C112×C37 ⋊ C22 |
| Sylow | C112 ⋊ C2×D37 |
| Sylow | C37 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C37 | C22 |
| LCS | G ▷ C112×C37 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 814 |
Polycyclic presentation:
2^2,11^2,37|c^a=c^10,e^a=e^36,c^b=c^10,d^b=d^101165 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17908, 26);