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D19⋊C3×C11⋊C25 #44535461

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

Aliases

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

Splittings

derived, HallC11×C19 ⋊ C2×C3×C25
HallC19⋊C3×C11⋊C25 ⋊ C2
HallD19×C11⋊C25 ⋊ C3
HallC19×C11⋊C25 ⋊ C2×C3
HallC11×D19⋊C3 ⋊ C25
HallC11×C19⋊C3 ⋊ C2×C25
HallC11×D19 ⋊ C3×C25
HallC19⋊C3 ⋊ C2×C11⋊C25
HallD19 ⋊ C3×C11⋊C25
SylowC19 ⋊ C2×C3×C11⋊C25
SylowC11 ⋊ C25×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC5C11⋊C5×D19⋊C3
commutator, hypocenterC11×C19C2×C3×C25
Fitting, socle, cosocleC5×C11×C19C2×C3×C5
prime radicalC5×C11×D19⋊C3C5
LCSG ▷ C11×C19
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5225

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 34);