Finite Group DatabasebetaFinite Group Databasebeta| order | 4860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | D5×#92300 |
| Fitting, Hall | C5×C32⋊H(3,𝔽3) ⋊ C22 |
| derived | C3×C5×H(3,𝔽3) ⋊ C22×C3 |
| Sylow | C32⋊H(3,𝔽3) ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×#92300 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×C3⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C3×C5×H(3,𝔽3) | C22×C3 |
| Frattini | C32 | C3×D5×C3⋊D3 |
| Fitting | C5×C32⋊H(3,𝔽3) | C22 |
| socle | C32×C5 | C2×C3×C3⋊D3 |
| LCS | G ▷ C3×C5×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
898 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 898 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#92300, D5×#13091120, D5×#11757730, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#92300, D5×#11757730, #72254531 |
| maximal quotient of | D5×#13091119 |
Past the SmallGroups library coverage — no SmallGroups id.