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C3×C101×AGL(1,𝔽11) #45686798

order33330
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C101 · Schur multiplier (H2) = C1

Aliases

direct productC3×C101×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×C101)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C101)
unambiguous semidirect product(C3×D11)⋊(C5×C101)

Splittings

Fitting, socle, HallC3×C11×C101 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C5×C101
HallC3×C11⋊C5×C101 ⋊ C2
HallC3×D11×C101 ⋊ C5
HallC11⋊C5×C101 ⋊ C2×C3
HallD11×C101 ⋊ C3×C5
HallC11×C101 ⋊ C2×C3×C5
HallC3×C11⋊C5 ⋊ C2×C101
HallC3×D11 ⋊ C5×C101
HallC11⋊C5 ⋊ C2×C3×C101
HallC3×C11 ⋊ C2×C5×C101
HallD11 ⋊ C3×C5×C101

Subgroups

subgroupG/H
center, hypercenterC3×C101AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C5×C101
FrattiniC1G
Fitting, socleC3×C11×C101C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C101

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3333

Conjugacy classes & character table

3333 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33330, 30);