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D55×C97⋊C3 #44544982

order32010
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productD55×C97⋊C3
unambiguous semidirect productC5⋊(D11×C97⋊C3)
unambiguous semidirect productC11⋊(D5×C97⋊C3)
unambiguous semidirect product(C97×D55)⋊C3

Splittings

Fitting, socle, derived, HallC5×C11×C97 ⋊ C2×C3
HallC5×C11×C97⋊C3 ⋊ C2
HallC97×D55 ⋊ C3
HallC11×C97⋊C3 ⋊ D5
HallC5×C97⋊C3 ⋊ D11
HallC11×C97 ⋊ C3×D5
HallC5×C97 ⋊ C3×D11
SylowC97 ⋊ C3×D55
HallC5×C11 ⋊ C2×C97⋊C3
SylowC11 ⋊ D5×C97⋊C3
SylowC5 ⋊ D11×C97⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C11×C97C2×C3
LCSG ▷ C5×C11×C97
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5335

Conjugacy classes & character table

1015 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 32);