Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C89 · Schur multiplier (H2) = C23 |
| direct product | C89×#1810 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C89 | C2×D4 |
| commutator | C2×C4 | C22×C4×C89 |
| Frattini, cosocle | C22×C4 | C23×C89 |
| socle | C22×C89 | C2×C4⋊C4 |
| prime radical | C24×C89 | Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C89 ◁ C23×C4×C89 ◁ G | |
292 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3916 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 542);