Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6480 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C9×C11×C19 |
| multiplicative | (ℤ/7961)ˣ, (ℤ/8303)ˣ, (ℤ/11313)ˣ, (ℤ/15922)ˣ, (ℤ/16606)ˣ, (ℤ/22626)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C3 | C22×C3×C11×C19 |
| socle | C22×C3×C11×C19 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
60 conjugacy classes of subgroups.
7524 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 13);