Finite Group DatabasebetaFinite Group Databasebeta| order | 26375 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C52 |
| unambiguous semidirect product | C52⋊(C211⋊C5) |
| unambiguous semidirect product | C211⋊H(3,𝔽5) |
| unambiguous semidirect product | (C5×C211⋊C5)⋊C5 |
| Fitting | C52×C211 ⋊ C5 |
| Sylow | C211 ⋊ H(3,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C5×C211⋊C5 |
| commutator, socle, cosocle | C5×C211 | C52 |
| Fitting | C52×C211 | C5 |
| hypercenter | C52 | C211⋊C5 |
| hypocenter | C211 | H(3,𝔽5) |
| LCS | G ▷ C5×C211 ▷ C211 | |
| UCS | C1 ◁ C5 ◁ C52 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5275 |
Polycyclic presentation:
5^3,211|b^a=bc,d^b=d^1071079 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26375, 9);