Finite Group DatabasebetaFinite Group Databasebeta| order | 8145 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#13108658 |
| Fitting, socle, Hall | C5×C181 ⋊ C9 |
| derived, Sylow | C181 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #13108658 |
| commutator, hypocenter | C181 | C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C5×C181 | C9 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
145 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#13108658⋊C2, C5⋊(#13108658⋊C2), D5×#13108658, … |
| maximal normal subgroup of | C5×#13108658⋊C2, C5⋊(#13108658⋊C2), D5×#13108658, … |
| maximal quotient of | C2×C5×#13108658, C5×C22⋊#13108658 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8145, 8);