Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C239 ⋊ C2 |
| Sylow | C239 ⋊ #453 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1912 |
Polycyclic presentation:
2^6,239|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^238,d^b=df,e^b=ef,d^c=df2039 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486530, #44486542, #44486552, … |
| maximal normal subgroup of | #44486530, #44486542, #44486552, … |
| maximal quotient of | #44483466, #44483471, #44483494, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 717);