Finite Group DatabasebetaFinite Group Databasebeta| order | 26780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C103⋊#63122 |
| Fitting, socle, derived, Hall | C5×C13×C103 ⋊ C4 |
| Hall | C13×C103 ⋊ AGL(1,𝔽5) |
| Hall | C5×C103 ⋊ #261 |
| Sylow | C103 ⋊ #63122 |
| Hall | C5×C13 ⋊ Dic103 |
| Sylow | C13 ⋊ C103⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C103⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C103 | C4 |
| prime radical, cosocle | C103×D65 | C2 |
| LCS | G ▷ C5×C13×C103 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6695 |
Polycyclic presentation:
2^2,5,13,103|a^2=b,c^a=c^2,d^a=d^5,e^a=e^102,c^b=c^4,d^b=d^121754 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26780, 16);