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C3×C97×AGL(1,𝔽11) #44544971

order32010
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C97 · Schur multiplier (H2) = C1

Aliases

direct productC3×C97×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×C97)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C97)
unambiguous semidirect product(C3×D11)⋊(C5×C97)
unambiguous semidirect product(C3×D11×C97)⋊C5

Splittings

Fitting, socle, HallC3×C11×C97 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C5×C97
HallC3×C11⋊C5×C97 ⋊ C2
HallC3×D11×C97 ⋊ C5
HallC11⋊C5×C97 ⋊ C2×C3
HallD11×C97 ⋊ C3×C5
HallC11×C97 ⋊ C2×C3×C5
HallC3×C11⋊C5 ⋊ C2×C97
HallC3×D11 ⋊ C5×C97
HallC11⋊C5 ⋊ C2×C3×C97
HallC3×C11 ⋊ C2×C5×C97
HallD11 ⋊ C3×C5×C97

Subgroups

subgroupG/H
center, hypercenterC3×C97AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C5×C97
FrattiniC1G
Fitting, socleC3×C11×C97C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C97

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3201

Conjugacy classes & character table

3201 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 21);