Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 688128 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C16 |
| abelian | C162×C29 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C82 | C22×C29 |
| socle | C22×C29 | C82 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
166 conjugacy classes of subgroups.
7424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C29×C32, C2×C162×C29, C3×C162×C29 |
| maximal normal subgroup of | C16×C29×C32, C2×C162×C29, C3×C162×C29 |
| maximal quotient of | C16×C29×C32, C2×C162×C29, C3×C162×C29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 39);