Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 319488 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C16×C79 |
| multiplicative | (ℤ/16167)ˣ, (ℤ/20288)ˣ, (ℤ/21556)ˣ, (ℤ/32334)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C23×C79 |
| socle, prime radical | C23×C79 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
10112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 837);