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Cayley diagram

AGL(1,𝔽5)×D11 #89190

order440
isoclinismisoclinic class of AGL(1,𝔽5)×D11
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽5)×D11
unambiguous semidirect product(C11×AGL(1,𝔽5))⋊C2
unambiguous semidirect product(C11⋊AGL(1,𝔽5))⋊C2

Splittings

Fitting, socle, derived, HallC5×C11 ⋊ C2×C4
SylowC11 ⋊ C2×AGL(1,𝔽5)
SylowC5 ⋊ C4×D11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11C2×C4
prime radicalD5×D11C2
cosocleD5×C11C22
LCSG ▷ C5×C11
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 55

A minimal faithful permutation representation — 2 generators on 16 points:

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

Conjugacy classes & character table

35 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×D11, C3×AGL(1,𝔽5)×D11, D11×ΓL(1,𝔽16), …
maximal normal subgroup ofC2×AGL(1,𝔽5)×D11, C3×AGL(1,𝔽5)×D11, AGL(1,𝔽5)×AGL(1,𝔽11), …
maximal quotient ofAGL(1,𝔽5)×Dic11, (C2×AGL(1,𝔽5))⋊D11, Dic11⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 43);