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Cayley diagram

C2×C11⋊AGL(1,𝔽5) #89193

order440
isoclinismisoclinic class of C11⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊AGL(1,𝔽5)
unambiguous semidirect productD5⋊Dic11
unambiguous semidirect product(C2×C11)⋊AGL(1,𝔽5)

Splittings

Fitting, socleC2×C5×C11 ⋊ C4
derived, HallC5×C11 ⋊ C2×C4
SylowC11 ⋊ C2×AGL(1,𝔽5)
SylowC5 ⋊ C2×Dic11

Subgroups

subgroupG/H
center, hypercenterC2C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C2×C4
FrattiniC1G
Fitting, socleC2×C5×C11C4
prime radicalC2×D5×C11C2
cosocleD5×C11C22
LCSG ▷ C5×C11
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 110

A minimal faithful permutation representation — 2 generators on 18 points:

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

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×Dic11, (C2×AGL(1,𝔽5))⋊D11, Dic11⋊AGL(1,𝔽5), …
maximal normal subgroup ofAGL(1,𝔽5)×Dic11, (C2×AGL(1,𝔽5))⋊D11, Dic11⋊AGL(1,𝔽5), …
maximal quotient ofD5⋊(C11⋊C8), #11724975, C4×C11⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 46);