Finite Group DatabasebetaFinite Group Databasebeta| order | 8145 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13108656⋊C5 |
| derived, Sylow | C181 ⋊ C5×C9 |
| Hall | #13108656 ⋊ C5 |
| Hall | C181⋊C5 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C181⋊C3)⋊C5 |
| commutator, hypocenter | C181 | C5×C9 |
| Fitting, socle | C3×C181 | C3×C5 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,181,3|a^3=d,c^a=c^48,c^b=c^5981 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13108656⋊C5, (#13108656⋊C2)⋊C5, C22⋊(#13108656⋊C5) |
| maximal normal subgroup of | C2×#13108656⋊C5, (#13108656⋊C2)⋊C5 |
| maximal quotient of | C2×#13108656⋊C5, C22⋊(#13108656⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8145, 2);