Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×#14268436 |
| Fitting, socle | C2×C32×C52 ⋊ C2×C4 |
| derived, Hall | C32×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×#624 |
| Sylow | C32 ⋊ C22×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #14268436 |
| commutator, hypocenter | C32×C52 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C2×C4 |
| prime radical | C2×C3⋊D3×C5⋊D5 | C2 |
| cosocle | C32×C5⋊D5 | C23 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
688 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 81 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 | D3×#14268436, C2×#72210392, #72224612, … |
| maximal normal subgroup of | C2×#72210392, #72224612, #72224627, … |
| maximal quotient of | D3×#14268436, #72224631, C22×#14268436, … |
Past the SmallGroups library coverage — no SmallGroups id.