Finite Group DatabasebetaFinite Group Databasebeta| order | 30660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊#13091734 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C73 | C3×C4 |
| prime radical | D5×ΓL(1,𝔽8)×C73 | C2 |
| cosocle | C7×D5×C73 | C2×C3 |
| LCS | G ▷ C5×C7×C73 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2555 |
Polycyclic presentation:
2,3,2,5,7,73|a^2=c,d^a=d^2,e^a=e^6,f^a=f^72,e^b=e^2,d^c=d^4739 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30660, 77);