Finite Group Databasebeta

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C11⋊C5×D109⋊C3 #49112594

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

Aliases

direct productC11⋊C5×D109⋊C3
unambiguous semidirect productD109⋊(C3×C11⋊C5)
unambiguous semidirect product(C109⋊C3)⋊(C2×C11⋊C5)
unambiguous semidirect product(C11×D109⋊C3)⋊C5
unambiguous semidirect product(C11⋊C5×D109)⋊C3

Splittings

Fitting, socle, derived, HallC11×C109 ⋊ C2×C3×C5
HallC11⋊C5×C109⋊C3 ⋊ C2
HallC11⋊C5×D109 ⋊ C3
HallC11×D109⋊C3 ⋊ C5
HallC11⋊C5×C109 ⋊ C2×C3
HallC11×C109⋊C3 ⋊ C2×C5
HallC11×D109 ⋊ C3×C5
HallC109⋊C3 ⋊ C2×C11⋊C5
HallD109 ⋊ C3×C11⋊C5
SylowC109 ⋊ C2×C3×C11⋊C5
SylowC11 ⋊ C5×D109⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C109C2×C3×C5
LCSG ▷ C11×C109
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1199

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35970, 34);