Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×C4⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #22683 |
986 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7552 |
Polycyclic presentation:
2^8,59|a^2=g,b^2=h,c^2=fh,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^58,d^b=de,e^b=eh,i^b=i^58,e^d=eh,i^d=i^582390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 187993);