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C97×C3⋊AGL(1,𝔽11) #44544975

order32010
automorphism?
homologyAbelianization (H1) = C2×C5×C97 · Schur multiplier (H2) = C1

Aliases

direct productC97×C3⋊AGL(1,𝔽11)
unambiguous semidirect productC3⋊(C97×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D3×C97)
unambiguous semidirect productD33⋊(C5×C97)
unambiguous semidirect product(D33×C97)⋊C5

Splittings

Fitting, socle, HallC3×C11×C97 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C97
HallC3×C11⋊C5×C97 ⋊ C2
HallD33×C97 ⋊ C5
HallC11⋊C5×C97 ⋊ D3
HallC11×C97 ⋊ C5×D3
HallC3×C97 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ C2×C97
HallD33 ⋊ C5×C97
HallC11⋊C5 ⋊ D3×C97
SylowC11 ⋊ C5×D3×C97
SylowC3 ⋊ C97×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC97C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C2×C5×C97
FrattiniC1G
Fitting, socleC3×C11×C97C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C97

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3201

Conjugacy classes & character table

1746 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 25);