Finite Group DatabasebetaFinite Group Databasebeta| order | 37700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C13×C25×C29 ⋊ C4 |
| Hall | C25×C29 ⋊ #261 |
| Hall | C13×C29 ⋊ #1035 |
| Hall | C13×C25 ⋊ Dic29 |
| Sylow | C29 ⋊ #13049907 |
| Sylow | C25 ⋊ #13094089 |
| Sylow | C13 ⋊ #15668504 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C25×C29 | C4 |
| Frattini | C5 | #21419476 |
| socle | C5×C13×C29 | AGL(1,𝔽5) |
| prime radical, cosocle | C29×D325 | C2 |
| LCS | G ▷ C13×C25×C29 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9425 |
Polycyclic presentation:
2^2,5,13,29,5|a^2=b,c^5=f,c^a=c^2f,d^a=d^8,e^a=e^28,f^a=f^2,c^b=c^4f^4,d^b=d^12,f^b=f^42381 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37700, 28);