Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C27 |
| direct product | C22×C41×#331 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C41 | C22⋊C4 |
| commutator | C2×C4 | C23×C4×C41 |
| Frattini, cosocle | C42 | C24×C41 |
| prime radical | C22×#127×C41 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C41 ◁ C22×C42×C41 ◁ G | |
2022 conjugacy classes of subgroups.
3116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10496, 10681);