Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D33×D5 |
| Fitting, socle, derived, Hall | C33×C5 ⋊ C24 |
| Sylow | C33 ⋊ C23×D5 |
| Sylow | C5 ⋊ C2×D33 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C33×C5 | C24 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 | |
1284 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
108 conjugacy classes — view the full character table.
| maximal subgroup of | D33×AGL(1,𝔽5), D3×#14268487, C2×D33×D5, … |
| maximal normal subgroup of | D33×AGL(1,𝔽5), C2×D33×D5 |
| maximal quotient of | D3×#14268487, C2×D33×D5, D3×D5×#624, … |
Past the SmallGroups library coverage — no SmallGroups id.