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D5⋊(C11⋊C8) #11724974

order880
isoclinismisoclinic class of C11⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD5⋊(C11⋊C8)

Splittings

derived, HallC5×C11 ⋊ C2×C8
SylowC11 ⋊ D5⋊C8
SylowC5 ⋊ C2×C11⋊C8

Subgroups

subgroupG/H
center, hypercenterC4C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C2×C8
FrattiniC2C2×C11⋊AGL(1,𝔽5)
FittingC4×C5×C11C4
socleC2×C5×C11C2×C4
prime radicalC2×D5×C11C4
cosocleC11×Dic5C22
LCSG ▷ C5×C11
UCSC1 ◁ C4

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 440

Polycyclic presentation:

2^4,5,11|a^2=c,b^2=d,c^2=d,e^a=e^3,f^a=f^10,e^c=e^4

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C11⋊C8, #13182557, #13182559, …
maximal normal subgroup ofAGL(1,𝔽5)×C11⋊C8, #13182557, #13182559, …
maximal quotient ofD5⋊(C11⋊C16), #13182636, C4×C11⋊#170, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 142);