Finite Group DatabasebetaFinite Group Databasebeta| order | 18180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C32×C101 ⋊ C22×C5 |
| derived | C3×C101 ⋊ C22×C3×C5 |
| Hall | C32×C101⋊C5 ⋊ C22 |
| Hall | C3×D3×D101 ⋊ C5 |
| Hall | C101⋊C5 ⋊ C2×C3×D3 |
| Sylow | C101 ⋊ C2×C3×C5×D3 |
| Sylow | C32 ⋊ C2×D101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D101⋊C5 |
| commutator, cosocle, hypocenter | C3×C101 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C101 | C22×C5 |
| LCS | G ▷ C3×C101 | |
| UCS | C1 ◁ C3 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 606 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18180, 70);