Finite Group Databasebeta

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D55×C109⋊C3 #49112592

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

Aliases

direct productD55×C109⋊C3
unambiguous semidirect productC5⋊(D11×C109⋊C3)
unambiguous semidirect productC11⋊(D5×C109⋊C3)
unambiguous semidirect product(C109×D55)⋊C3

Splittings

Fitting, socle, derived, HallC5×C11×C109 ⋊ C2×C3
HallC5×C11×C109⋊C3 ⋊ C2
HallC109×D55 ⋊ C3
HallC11×C109⋊C3 ⋊ D5
HallC5×C109⋊C3 ⋊ D11
HallC11×C109 ⋊ C3×D5
HallC5×C109 ⋊ C3×D11
SylowC109 ⋊ C3×D55
HallC5×C11 ⋊ C2×C109⋊C3
SylowC11 ⋊ D5×C109⋊C3
SylowC5 ⋊ D11×C109⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C11×C109C2×C3
LCSG ▷ C5×C11×C109
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5995

Conjugacy classes & character table

1131 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35970, 32);