Finite Group DatabasebetaFinite Group Databasebeta| order | 25216 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#117×C197 ⋊ C2 |
| Sylow | C197 ⋊ #3449 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D197 |
| commutator, socle, cosocle | C22×C197 | C25 |
| Frattini | C22 | C24×D197 |
| Fitting | C2×#117×C197 | C2 |
| hypercenter | C2×#117 | D197 |
| hypocenter | C197 | #3449 |
| LCS | G ▷ C22×C197 ▷ C197 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#117 | |
1556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6304 |
Polycyclic presentation:
2^7,197|e^2=f,b^a=bf,c^a=cg,d^a=df,h^a=h^196,c^b=cf,h^c=h^1963964 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25216, 17843);