Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C41 · Schur multiplier (H2) = C22 |
| direct product | C41×#7194 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | #99 |
| commutator | C2×C4 | C4×C8×C41 |
| Frattini, cosocle | C22×M16 | C22×C41 |
| socle | C22×C41 | #323 |
| prime radical | C24×C41 | M16 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ C22×C4×C41 ◁ C22×M16×C41 ◁ G | |
310 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 310 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.
2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 182);