Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×#87641 |
| Hall | C32×C72 ⋊ D4 |
| Sylow | C72 ⋊ C32×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D72 |
| commutator, cosocle | C2×C72 | C22×C32 |
| Frattini | C2 | C32×D72 |
| Fitting, socle | C2×C32×C72 | C22 |
| hypocenter | C72 | C32×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2×C32 | |
282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 252 |
423 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#11924176, C32×#11716115 |
| maximal normal subgroup of | C32×#11924176, C32×#11716115 |
Past the SmallGroups library coverage — no SmallGroups id.