Finite Group DatabasebetaFinite Group Databasebeta| order | 8004 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7392 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C3×C23×C29 |
| multiplicative | (ℤ/8201)ˣ, (ℤ/12009)ˣ, (ℤ/16012)ˣ, (ℤ/16402)ˣ, (ℤ/24018)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
40 conjugacy classes of subgroups.
8004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8004, 9);