Finite Group Databasebeta

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C2×C4×C11×AGL(1,𝔽5) #13183334

order1760
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×C11×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C42×C11)

Splittings

FittingC2×C4×C5×C11 ⋊ C4
derived, SylowC5 ⋊ C2×C42×C11
HallC5×C11 ⋊ C2×C42

Subgroups

subgroupG/H
center, hypercenterC2×C4×C11AGL(1,𝔽5)
commutator, hypocenterC5C2×C42×C11
FrattiniC2C22×C11×AGL(1,𝔽5)
FittingC2×C4×C5×C11C4
socleC22×C5×C11C2×C4
prime radicalC22×D5×C11C22
cosocleC2×D5C23×C11
LCSG ▷ C5
UCSC1 ◁ C2×C4×C11

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 440

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1143);