Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5376000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C251 |
| multiplicative | (ℤ/20120)ˣ, (ℤ/24144)ˣ, (ℤ/30180)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2 | C24×C251 |
| socle | C24×C251 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
236 conjugacy classes of subgroups.
8032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 45);