Finite Group DatabasebetaFinite Group Databasebeta| order | 10496 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1705 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C41 · Schur multiplier (H2) = C25×C8 |
| direct product | C2×C41×#1712 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C41 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G | |
1342 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, 12589);