Finite Group DatabasebetaFinite Group Databasebeta| order | 7692 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C3×C641 |
| multiplicative | (ℤ/8981)ˣ, (ℤ/11541)ˣ, (ℤ/11547)ˣ, (ℤ/15388)ˣ, (ℤ/17962)ˣ, (ℤ/23082)ˣ, (ℤ/23094)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
20 conjugacy classes of subgroups.
7692 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7692, 5);