Finite Group DatabasebetaFinite Group Databasebeta| order | 9100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#13049907 |
| Fitting, derived, Hall | C7×C13×C25 ⋊ C4 |
| Hall | C13×C25 ⋊ Dic7 |
| Hall | C7×C25 ⋊ #261 |
| Hall | C7×C13 ⋊ #1035 |
| Sylow | C25 ⋊ C7⋊#261 |
| Sylow | C13 ⋊ C7⋊#1035 |
| Sylow | C7 ⋊ #13049907 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C13×C25 | C4 |
| Frattini | C5 | C7⋊#63121 |
| socle | C5×C7×C13 | AGL(1,𝔽5) |
| LCS | G ▷ C7×C13×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,7,13,5|a^2=b,c^5=f,c^a=c^2f,d^a=d^6,e^a=e^8,f^a=f^2,c^b=c^4f^4,e^b=e^12,f^b=f^4577 conjugacy classes — view the full character table.
| maximal subgroup of | #41031178, #41031179, ΓL(1,𝔽8)⋊#13049907, … |
| maximal normal subgroup of | #41031178, #41031179, ΓL(1,𝔽8)⋊#13049907, … |
| maximal quotient of | C3×C7⋊#13049907, C3⋊(C7⋊#13049907) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9100, 17);