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C11×C22⋊AGL(1,𝔽5) #11724973

order880
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C22

Aliases

direct productC11×C22⋊AGL(1,𝔽5)
unambiguous semidirect productC22⋊(C11×AGL(1,𝔽5))
unambiguous semidirect product(C2×AGL(1,𝔽5))⋊(C2×C11)

Splittings

FittingC22×C5×C11 ⋊ C4
HallC5×C11 ⋊ C22⋊C4
SylowC5 ⋊ C11×C22⋊C4

Subgroups

subgroupG/H
centerC2×C11C2×AGL(1,𝔽5)
commutatorC2×C5C2×C4×C11
FrattiniC2C2×C11×AGL(1,𝔽5)
FittingC22×C5×C11C4
socleC2×C5×C11C2×C4
prime radicalC22×D5×C11C2
cosocleC2×D5C22×C11
hypercenterC22×C11AGL(1,𝔽5)
hypocenterC5C11×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ C22×C11

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 220

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15)(18,20);(13,14,15,16)(17,18)(19,20)

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13182580, #13182581, C11×#3999, …
maximal normal subgroup of#13182580, #13182581, C11×#3999, …
maximal quotient ofC11×#3999, C11×#4003, C11×#4005, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 141);