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C5×C11×D109⋊C3 #49112587

order35970
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D109⋊C3
unambiguous semidirect productD109⋊(C3×C5×C11)
unambiguous semidirect product(C109⋊C3)⋊(C2×C5×C11)
unambiguous semidirect product(C5×D109)⋊(C3×C11)
unambiguous semidirect product(C5×C11×D109)⋊C3

Splittings

Fitting, socle, HallC5×C11×C109 ⋊ C2×C3
derived, SylowC109 ⋊ C2×C3×C5×C11
HallC5×C11×C109⋊C3 ⋊ C2
HallC5×C11×D109 ⋊ C3
HallC11×C109⋊C3 ⋊ C2×C5
HallC11×D109 ⋊ C3×C5
HallC5×C109⋊C3 ⋊ C2×C11
HallC11×C109 ⋊ C2×C3×C5
HallC5×D109 ⋊ C3×C11
HallC5×C109 ⋊ C2×C3×C11
HallC109⋊C3 ⋊ C2×C5×C11
HallD109 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11D109⋊C3
commutator, cosocle, hypocenterC109C2×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C109C2×C3
LCSG ▷ C109
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5995

Conjugacy classes & character table

1320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35970, 27);