Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C241 ⋊ #544 |
206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|a^2=f,b^2=e,c^2=f,b^a=be,c^a=cf,d^a=de,g^a=g^240,c^b=ce2422 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44506384, #44506387, #44506418, … |
| maximal normal subgroup of | #44506384, #44506387, #44506418, … |
| maximal quotient of | #44510063, #44510069 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1180);