Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#13133324 |
| Fitting, derived, Hall | C7×C17×C25 ⋊ C4 |
| Hall | C17×C25 ⋊ Dic7 |
| Hall | C7×C25 ⋊ #595 |
| Hall | C7×C17 ⋊ #1035 |
| Sylow | C25 ⋊ C7⋊#595 |
| Sylow | C17 ⋊ C7⋊#1035 |
| Sylow | C7 ⋊ #13133324 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C17×C25 | C4 |
| Frattini | C5 | C7⋊#66776 |
| socle | C5×C7×C17 | AGL(1,𝔽5) |
| prime radical, cosocle | C7×D425 | C2 |
| LCS | G ▷ C7×C17×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,7,17,5|a^2=b,c^5=f,c^a=c^2f,d^a=d^6,e^a=e^4,f^a=f^2,c^b=c^4f^4,e^b=e^16,f^b=f^4752 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊#13133324, C3×C7⋊#13133324, C3⋊(C7⋊#13133324) |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊#13133324, C3×C7⋊#13133324 |
| maximal quotient of | C3×C7⋊#13133324, C3⋊(C7⋊#13133324) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 19);