Finite Group DatabasebetaFinite Group Databasebeta| order | 25216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #478×C197 ⋊ C2 |
| Sylow | C197 ⋊ #3123 |
394 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6304 |
Polycyclic presentation:
2^7,197|a^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^196,d^b=dg,h^b=h^196,f^c=fg,h^d=h^1961894 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25216, 14764);