Finite Group DatabasebetaFinite Group Databasebeta| order | 2430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×#92338 |
| Fitting, Hall | C5×C32⋊H(3,𝔽3) ⋊ C2 |
| derived, Sylow | C32⋊H(3,𝔽3) ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C32×C5 | C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C32⋊H(3,𝔽3) | C2×C5 |
| Frattini | C32 | C5×C3⋊(C3⋊D3) |
| Fitting | C5×C32⋊H(3,𝔽3) | C2 |
| LCS | G ▷ C32⋊H(3,𝔽3) | |
| UCS | C1 ◁ C32×C5 | |
534 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#92338, C5×#11757730, #72254502, … |
| maximal normal subgroup of | D5×#92338, C5×#11757730, #72254502, … |
| maximal quotient of | C5×#13091120 |
Past the SmallGroups library coverage — no SmallGroups id.