Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| isoclinism | isoclinic class of C7⋊#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C7⋊#595 |
| unambiguous semidirect product | C7⋊(C25×#595) |
| Fitting, Hall | C7×C17×C25 ⋊ C4 |
| derived, Hall | C7×C17 ⋊ C4×C25 |
| Hall | C17×C25 ⋊ Dic7 |
| Hall | C7×C25 ⋊ #595 |
| Sylow | C17 ⋊ C25×Dic7 |
| Sylow | C7 ⋊ C25×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C7⋊#595 |
| commutator, hypocenter | C7×C17 | C4×C25 |
| Frattini | C5 | C5×C7⋊#595 |
| Fitting | C7×C17×C25 | C4 |
| socle | C5×C7×C17 | C4×C5 |
| prime radical, cosocle | C5×C7×D17 | C2×C5 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
950 conjugacy classes — view the full character table.
| maximal subgroup of | C25×ΓL(1,𝔽8)⋊#595, C3×C25×C7⋊#595, C25×C3⋊(C7⋊#595) |
| maximal normal subgroup of | C25×ΓL(1,𝔽8)⋊#595, C3×C25×C7⋊#595 |
| maximal quotient of | C3×C25×C7⋊#595, C25×C3⋊(C7⋊#595) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 11);