Finite Group DatabasebetaFinite Group Databasebeta| order | 27004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C43⋊#10597845 |
| Fitting, socle, derived, Hall | C43×C157 ⋊ C4 |
| Sylow | C157 ⋊ Dic43 |
| Sylow | C43 ⋊ #10597845 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C43×C157 | C4 |
| prime radical, cosocle | C43×D157 | C2 |
| LCS | G ▷ C43×C157 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6751 |
Polycyclic presentation:
2^2,43,157|a^2=b,c^a=c^42,d^a=d^28,d^b=d^1561723 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27004, 7);