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C5⋊AGL(1,𝔽67) #36348649

order22110
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊AGL(1,𝔽67)
unambiguous semidirect product(C5⋊(D67⋊C3))⋊C11
unambiguous semidirect product((C67⋊C3)⋊C11)⋊D5
unambiguous semidirect product(C5⋊(D67⋊C11))⋊C3

Splittings

Fitting, socle, derived, HallC5×C67 ⋊ C2×C3×C11
HallC5×(C67⋊C3)⋊C11 ⋊ C2
HallC5⋊(D67⋊C11) ⋊ C3
HallC5×C67⋊C11 ⋊ C2×C3
Hall(C67⋊C3)⋊C11 ⋊ D5
HallC5⋊(D67⋊C3) ⋊ C11
HallC5×C67⋊C3 ⋊ C2×C11
HallC67⋊C11 ⋊ C3×D5
HallD335 ⋊ C3×C11
HallC67⋊C3 ⋊ D5×C11
SylowC67 ⋊ C3×D5×C11
SylowC5 ⋊ AGL(1,𝔽67)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C67C2×C3×C11
LCSG ▷ C5×C67
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 335

Polycyclic presentation:

2,3,5,11,67|c^a=c^4,e^a=e^66,e^b=e^37,e^d=e^64

Conjugacy classes & character table

137 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22110, 45);