Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1156055040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C24×C4×C113 |
| multiplicative | (ℤ/27240)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2 | C25×C113 |
| socle | C25×C113 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1362 conjugacy classes of subgroups.
7232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 260);