Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C239 ⋊ C2 |
| Sylow | C239 ⋊ #405 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=d,b^2=e,d^2=f,g^a=g^238,c^b=cf,g^c=g^2382420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486151, #44486362 |
| maximal normal subgroup of | #44486151, #44486362 |
| maximal quotient of | #44482827, #44482833, #44482834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 506);