Finite Group DatabasebetaFinite Group Databasebeta| order | 17908 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊#3866) |
| Fitting, socle, derived, Hall | C112×C37 ⋊ C4 |
| Sylow | C112 ⋊ #3866 |
| Sylow | C37 ⋊ C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C37 | C4 |
| prime radical, cosocle | C112×D37 | C2 |
| LCS | G ▷ C112×C37 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4477 |
Polycyclic presentation:
2^2,11^2,37|a^2=b,c^a=c^10,d^a=d^10,e^a=e^31,e^b=e^361213 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17908, 22);