Finite Group DatabasebetaFinite Group Databasebeta| order | 32108 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#13063703 |
| Fitting, socle, derived, Hall | C23×C349 ⋊ C4 |
| Sylow | C349 ⋊ Dic23 |
| Sylow | C23 ⋊ #13063703 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C23×C349 | C4 |
| prime radical, cosocle | C23×D349 | C2 |
| LCS | G ▷ C23×C349 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8027 |
Polycyclic presentation:
2^2,23,349|a^2=b,c^a=c^22,d^a=d^136,d^b=d^3482027 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32108, 7);