Finite Group DatabasebetaFinite Group Databasebeta| order | 34356 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C7⋊#13109888) |
| unambiguous semidirect product | C7⋊(C3⋊#13109888) |
| Fitting, socle, derived, Hall | C3×C7×C409 ⋊ C4 |
| Hall | C7×C409 ⋊ Dic3 |
| Hall | C3×C409 ⋊ Dic7 |
| Sylow | C409 ⋊ Dic21 |
| Hall | C3×C7 ⋊ #13109888 |
| Sylow | C7 ⋊ C3⋊#13109888 |
| Sylow | C3 ⋊ C7⋊#13109888 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C409 | C4 |
| prime radical, cosocle | C3×C7×D409 | C2 |
| LCS | G ▷ C3×C7×C409 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8589 |
Polycyclic presentation:
2^2,3,7,409|a^2=b,c^a=c^2,d^a=d^6,e^a=e^266,e^b=e^4082166 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34356, 55);