Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C3⋊D3×#6038 |
| Hall | C32×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ D4×C3⋊D3 |
| Sylow | C32 ⋊ C2×#6038 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D52×C3⋊D3 |
| commutator, Fitting, socle, cosocle | C2×C32×C52 | C23 |
| hypocenter | C32×C52 | C2×D4 |
| LCS | G ▷ C2×C32×C52 ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
840 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#87886, C2×C3⋊D3×#6038 |
| maximal normal subgroup of | C3⋊D3×#87886, C2×C3⋊D3×#6038 |
| maximal quotient of | C2×C3⋊D3×#6038 |
Past the SmallGroups library coverage — no SmallGroups id.