Finite Group Databasebeta

← Prev (#36348646) Next (#36348648) →

C5×AGL(1,𝔽67) #36348647

order22110
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽67)
unambiguous semidirect product(D67⋊C3)⋊(C5×C11)
unambiguous semidirect product(D67⋊C11)⋊(C3×C5)
unambiguous semidirect product(C5×D67⋊C3)⋊C11
unambiguous semidirect product((C67⋊C3)⋊C11)⋊(C2×C5)
unambiguous semidirect product(C5×D67⋊C11)⋊C3

Splittings

Fitting, socle, HallC5×C67 ⋊ C2×C3×C11
derived, SylowC67 ⋊ C2×C3×C5×C11
HallC5×(C67⋊C3)⋊C11 ⋊ C2
HallC5×D67⋊C11 ⋊ C3
HallC5×C67⋊C11 ⋊ C2×C3
Hall(C67⋊C3)⋊C11 ⋊ C2×C5
HallC5×D67⋊C3 ⋊ C11
HallD67⋊C11 ⋊ C3×C5
HallC5×C67⋊C3 ⋊ C2×C11
HallC67⋊C11 ⋊ C2×C3×C5
HallC5×D67 ⋊ C3×C11
HallD67⋊C3 ⋊ C5×C11
HallC67⋊C3 ⋊ C2×C5×C11
HallD67 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5AGL(1,𝔽67)
commutator, cosocle, hypocenterC67C2×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C67C2×C3×C11
LCSG ▷ C67
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 335

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22110, 43);