Finite Group Databasebeta

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D3×C19×C11⋊C25 #44535450

order31350
automorphism?
homologyAbelianization (H1) = C2×C19×C25 · Schur multiplier (H2) = C1

Aliases

direct productD3×C19×C11⋊C25
unambiguous semidirect productC3⋊(C2×C19×C11⋊C25)
unambiguous semidirect product(D3×C11)⋊(C19×C25)
unambiguous semidirect product(D3×C11×C19)⋊C25

Splittings

derived, HallC3×C11 ⋊ C2×C19×C25
HallC3×C19×C11⋊C25 ⋊ C2
HallD3×C11×C19 ⋊ C25
HallC3×C11⋊C25 ⋊ C2×C19
HallC3×C11×C19 ⋊ C2×C25
HallC11×C19 ⋊ D3×C25
HallD3×C11 ⋊ C19×C25
HallC3×C19 ⋊ C2×C11⋊C25
SylowC11 ⋊ D3×C19×C25
SylowC3 ⋊ C2×C19×C11⋊C25

Subgroups

subgroupG/H
center, hypercenterC5×C19D3×C11⋊C5
commutator, hypocenterC3×C11C2×C19×C25
FrattiniC5D3×C19×C11⋊C5
Fitting, socleC3×C5×C11×C19C2×C5
prime radicalC5×D3×C11×C19C5
cosocleC3×C5×C11C2×C5×C19
LCSG ▷ C3×C11
UCSC1 ◁ C5×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

1995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 23);