Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#13133324 |
| Fitting, derived, Hall | C3×C17×C25 ⋊ C4 |
| Hall | C17×C25 ⋊ Dic3 |
| Hall | C3×C25 ⋊ #595 |
| Hall | C3×C17 ⋊ #1035 |
| Sylow | C25 ⋊ C3⋊#595 |
| Sylow | C17 ⋊ C3⋊#1035 |
| Sylow | C3 ⋊ #13133324 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C17×C25 | C4 |
| Frattini | C5 | C3⋊#66776 |
| socle | C3×C5×C17 | AGL(1,𝔽5) |
| LCS | G ▷ C3×C17×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,17,5|a^2=b,d^5=f^2,c^a=c^2,d^a=d^3f,e^a=e^13,f^a=f^3,d^b=d^4f^3,e^b=e^16,f^b=f^4324 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#13133324, C3×C3⋊#13133324, C3⋊(C3⋊#13133324), … |
| maximal normal subgroup of | C3×C3⋊#13133324, C7×C3⋊#13133324 |
| maximal quotient of | C9⋊#13133324, C3×C3⋊#13133324, C3⋊(C3⋊#13133324), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 19);