Finite Group DatabasebetaFinite Group Databasebeta| order | 25625 |
| automorphism | ? |
| homology | Abelianization (H1) = C53 · Schur multiplier (H2) = C54 |
| direct product | C5×C52⋊(C41⋊C5) |
| unambiguous semidirect product | (C5×C41)⋊H(3,𝔽5) |
| Fitting | C53×C41 ⋊ C5 |
| Sylow | C41 ⋊ C5×H(3,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center | C52 | C5×C41⋊C5 |
| commutator, cosocle | C5×C41 | C53 |
| Frattini | C5 | C52×C41⋊C5 |
| Fitting | C53×C41 | C5 |
| socle | C52×C41 | C52 |
| hypercenter | C53 | C41⋊C5 |
| hypocenter | C41 | C5×H(3,𝔽5) |
| LCS | G ▷ C5×C41 ▷ C41 | |
| UCS | C1 ◁ C52 ◁ C53 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5125 |
1145 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25625, 49);