Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C4×C4⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #34816 |
1918 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7552 |
Polycyclic presentation:
2^8,59|a^2=fh,b^2=f,c^2=f,d^2=f,e^2=g,b^a=bf,c^a=cg,i^a=i^58,c^b=ch,d^b=dh2396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 339568);