Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C79 · Schur multiplier (H2) = C22 |
| direct product | C2×SD64×C79 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | D16 |
| commutator, Frattini, cosocle | C16 | C23×C79 |
| prime radical | C2×D16×C79 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C4×C79 ◁ C2×C8×C79 ◁ C2×C16×C79 ◁ G | |
112 conjugacy classes of subgroups.
3002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 992);