Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#13133324 |
| Fitting, Hall | C7×C17×C25 ⋊ C4 |
| derived, Hall | C17×C25 ⋊ C4×C7 |
| Hall | C7×C25 ⋊ #595 |
| Hall | C7×C17 ⋊ #1035 |
| Sylow | C25 ⋊ C7×#595 |
| Sylow | C17 ⋊ C7×#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13133324 |
| commutator, hypocenter | C17×C25 | C4×C7 |
| Frattini | C5 | C7×#66776 |
| Fitting | C7×C17×C25 | C4 |
| socle | C5×C7×C17 | AGL(1,𝔽5) |
| prime radical | C7×D425 | C2 |
| cosocle | D425 | C2×C7 |
| LCS | G ▷ C17×C25 | |
| UCS | C1 ◁ C7 | |
36 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#13133324, C3×C7×#13133324, C7×C3⋊#13133324 |
| maximal normal subgroup of | ΓL(1,𝔽8)×#13133324, C3×C7×#13133324 |
| maximal quotient of | C3×C7×#13133324, C7×C3⋊#13133324 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 15);