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C5×C11⋊(D97⋊C3) #44544979

order32010
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊(D97⋊C3)
unambiguous semidirect product(C97⋊C3)⋊(C5×D11)
unambiguous semidirect product(C5×D1067)⋊C3

Splittings

Fitting, socle, HallC5×C11×C97 ⋊ C2×C3
derived, HallC11×C97 ⋊ C2×C3×C5
HallC5×C11×C97⋊C3 ⋊ C2
HallC5×D1067 ⋊ C3
HallC11×C97⋊C3 ⋊ C2×C5
HallD1067 ⋊ C3×C5
HallC5×C97⋊C3 ⋊ D11
HallC5×C97 ⋊ C3×D11
HallC97⋊C3 ⋊ C5×D11
SylowC97 ⋊ C3×C5×D11
HallC5×C11 ⋊ D97⋊C3
SylowC11 ⋊ C5×D97⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C11⋊(D97⋊C3)
commutator, cosocle, hypocenterC11×C97C2×C3×C5
FrattiniC1G
Fitting, socleC5×C11×C97C2×C3
LCSG ▷ C11×C97
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5335

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 29);