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AGL(1,𝔽11)×C67⋊C3 #36348651

order22110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽11)×C67⋊C3
unambiguous semidirect productD11⋊(C5×C67⋊C3)
unambiguous semidirect product(C11⋊C5)⋊(C2×C67⋊C3)
unambiguous semidirect product(D11×C67⋊C3)⋊C5
unambiguous semidirect product(C67×AGL(1,𝔽11))⋊C3

Splittings

Fitting, socle, derived, HallC11×C67 ⋊ C2×C3×C5
HallC11⋊C5×C67⋊C3 ⋊ C2
HallC67×AGL(1,𝔽11) ⋊ C3
HallD11×C67⋊C3 ⋊ C5
HallC11⋊C5×C67 ⋊ C2×C3
HallC11×C67⋊C3 ⋊ C2×C5
HallD11×C67 ⋊ C3×C5
SylowC67 ⋊ C3×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×C67⋊C3
HallD11 ⋊ C5×C67⋊C3
SylowC11 ⋊ C2×C5×C67⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C67C2×C3×C5
LCSG ▷ C11×C67
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 737

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22110, 47);