Finite Group Databasebeta

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C11×C25×D19⋊C3 #44535454

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×D19⋊C3
unambiguous semidirect productD19⋊(C3×C11×C25)
unambiguous semidirect product(C19⋊C3)⋊(C2×C11×C25)
unambiguous semidirect product(C25×D19)⋊(C3×C11)
unambiguous semidirect product(C11×C25×D19)⋊C3

Splittings

Fitting, HallC11×C19×C25 ⋊ C2×C3
derived, SylowC19 ⋊ C2×C3×C11×C25
HallC11×C25×C19⋊C3 ⋊ C2
HallC11×C25×D19 ⋊ C3
HallC25×C19⋊C3 ⋊ C2×C11
HallC25×D19 ⋊ C3×C11
HallC11×C19⋊C3 ⋊ C2×C25
HallC19×C25 ⋊ C2×C3×C11
HallC11×D19 ⋊ C3×C25
HallC11×C19 ⋊ C2×C3×C25
HallC19⋊C3 ⋊ C2×C11×C25
HallD19 ⋊ C3×C11×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25D19⋊C3
commutator, hypocenterC19C2×C3×C11×C25
FrattiniC5C5×C11×D19⋊C3
FittingC11×C19×C25C2×C3
socleC5×C11×C19C2×C3×C5
prime radicalC5×C11×D19⋊C3C5
cosocleC5×C19C2×C3×C5×C11
LCSG ▷ C19
UCSC1 ◁ C11×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5225

Conjugacy classes & character table

2475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 27);