Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C241 ⋊ H(3,ℤ/4) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3856 |
Polycyclic presentation:
2^6,241|a^2=d,b^2=e,c^2=f,b^a=bc,e^a=ef,d^b=df,g^b=g^2402422 conjugacy classes. The character table is too large to display.
| maximal subgroup of | H(3,ℤ/4)×D241, C2×#29507473, #44507199, … |
| maximal normal subgroup of | H(3,ℤ/4)×D241, C2×#29507473, #44507199, … |
| maximal quotient of | #44505273, #44505274, #44505275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 305);