Finite Group DatabasebetaFinite Group Databasebeta| order | 2700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C33 |
| direct product | C5×D5×C3⋊(C3⋊D3) |
| Fitting, socle, Hall | C33×C52 ⋊ C22 |
| derived | C33×C5 ⋊ C22×C5 |
| Sylow | C33 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×C3⋊(C3⋊D3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C33×C5 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C33×C52 | C22 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 ◁ C5 | |
672 conjugacy classes of subgroups.
| transitive degree | μt(G) = 270 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D52×C3⋊(C3⋊D3), C5×D3×D5×C3⋊D3, D5×D15⋊(C3⋊D3) |
| maximal normal subgroup of | D52×C3⋊(C3⋊D3), C5×D3×D5×C3⋊D3, D5×D15⋊(C3⋊D3) |
Past the SmallGroups library coverage — no SmallGroups id.