Finite Group DatabasebetaFinite Group Databasebeta| order | 3424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C107 ⋊ #125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D107 |
| commutator, socle, prime radical, cosocle | C22×C107 | C23 |
| Fitting | C42×C107 | C2 |
| hypercenter | C42 | D107 |
| hypocenter | C107 | #125 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ C42 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3424 |
Polycyclic presentation:
2^5,107|a^2=d,b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^106862 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3424, 138);