Finite Group DatabasebetaFinite Group Databasebeta| order | 8145 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#13108656 |
| derived, Sylow | C181 ⋊ C5×C9 |
| Hall | C5×C181 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C181⋊C3 |
| commutator, hypocenter | C181 | C5×C9 |
| Frattini | C3 | C5×C181⋊C3 |
| Fitting, socle | C3×C5×C181 | C3 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C3×C5 | |
12 conjugacy classes of subgroups.
945 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×#13108656, C5×#13108656⋊C2, D5×#13108656, … |
| maximal normal subgroup of | C2×C5×#13108656, C5×#13108656⋊C2, D5×#13108656, … |
| maximal quotient of | C2×C5×#13108656, C5×C22⋊#13108656 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8145, 4);