Finite Group DatabasebetaFinite Group Databasebeta| order | 1300 |
| isoclinism | isoclinic class of #13049907 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C13×C25 ⋊ C4 |
| Sylow | C25 ⋊ #261 |
| Sylow | C13 ⋊ #1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C25 | C4 |
| Frattini | C5 | #63121 |
| socle | C5×C13 | AGL(1,𝔽5) |
| prime radical, cosocle | D325 | C2 |
| LCS | G ▷ C13×C25 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 325 |
Polycyclic presentation:
2^2,5,13,5|a^2=b,c^5=e,c^a=c^2e,d^a=d^8,e^a=e^2,c^b=c^4e^4,d^b=d^12,e^b=e^485 conjugacy classes — view the full character table.
| maximal subgroup of | #13049907⋊C3, C3×#13049907, C3⋊#13049907, … |
| maximal normal subgroup of | #13049907⋊C3, C3×#13049907, C11×#13049907, … |
| maximal quotient of | C3×#13049907, C3⋊#13049907, #26043328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1300, 9);