Finite Group DatabasebetaFinite Group Databasebeta| order | 6250 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, Sylow | #15691059 ⋊ C2 |
| derived | C5×C25 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11929369 |
| commutator, hypocenter | C5×C25 | C2×C25 |
| Frattini, socle | C53 | C5×D5 |
| Fitting | #15691059 | C2 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 ◁ C5 | |
124 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^5|b^5=e,c^5=f,b^a=bcef^2,c^a=c^4e^3f^3,d^a=d^4,e^a=ef,f^a=f^4,c^b=cd400 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6250, 79);