Finite Group DatabasebetaFinite Group Databasebeta| order | 32844 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C23⋊#595) |
| unambiguous semidirect product | C23⋊(ΓL(1,𝔽8)⋊#595) |
| unambiguous semidirect product | (C7⋊(C23⋊#595))⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C17×C23 | C3×C4 |
| prime radical | ΓL(1,𝔽8)×C23×D17 | C2 |
| cosocle | C7×C23×D17 | C2×C3 |
| LCS | G ▷ C7×C17×C23 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2737 |
Polycyclic presentation:
2,3,2,7,17,23|a^2=c,d^a=d^6,e^a=e^13,f^a=f^22,d^b=d^4,e^c=e^16584 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32844, 28);