Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C241 ⋊ C2 |
| Sylow | C241 ⋊ B(4,𝔽2) |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1928 |
Polycyclic presentation:
2^6,241|b^a=bd,c^a=ce,g^a=g^240,e^b=ef,d^c=df2056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44509427, #44509428, #44509432, … |
| maximal normal subgroup of | #44509427, #44509428, #44509432, … |
| maximal quotient of | #44506363, #44506368, #44506374, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 736);