Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C41 · Schur multiplier (H2) = C24 |
| direct product | C41×#12589 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | C2×#99 |
| commutator | C2×C4 | C2×C42×C41 |
| Frattini, cosocle | C2×#41 | C23×C41 |
| socle | C2×C41 | C2×#342 |
| prime radical | C22×#41×C41 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C22×C4×C41 ◁ C22×#41×C41 ◁ G | |
752 conjugacy classes of subgroups.
1886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 5577);