Finite Group DatabasebetaFinite Group Databasebeta| order | 5408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D4×D132 |
| Fitting | D4×C132 ⋊ C22 |
| Sylow | C132 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D132 |
| commutator, socle, cosocle | C2×C132 | C24 |
| Fitting | D4×C132 | C22 |
| hypercenter | D4 | D132 |
| hypocenter | C132 | C22×D4 |
| LCS | G ▷ C2×C132 ▷ C132 | |
| UCS | C1 ◁ C2 ◁ D4 | |
634 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×D13⋊#261, #72259301, #72259308, … |
| maximal normal subgroup of | D4×D13⋊#261, #72259301, #72259308, … |
Past the SmallGroups library coverage — no SmallGroups id.