Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 86016 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C29×C64 |
| multiplicative | (ℤ/15104)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C32 | C23×C29 |
| socle | C23×C29 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
142 conjugacy classes of subgroups.
7424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C29×C128, C2×C4×C29×C64, C23×C29×C64, … |
| maximal normal subgroup of | C22×C29×C128, C2×C4×C29×C64, C23×C29×C64, … |
| maximal quotient of | C22×C29×C128, C2×C4×C29×C64, C23×C29×C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 6723);