Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #106×C239 ⋊ C2 |
| Sylow | C239 ⋊ #442 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=e,c^2=ef,d^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^b=g^238,g^c=g^2381688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486443, #44486445 |
| maximal normal subgroup of | #44486443, #44486445 |
| maximal quotient of | #44483371, #44483411, #44483461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 660);