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Cayley diagram

C5×C11⋊C5 #63277

order275
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C11⋊C5
unambiguous semidirect productC11⋊C52
unambiguous semidirect product(C5×C11)⋊C5

Splittings

Fitting, socleC5×C11 ⋊ C5
derived, SylowC11 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC5C11⋊C5
commutator, cosocle, hypocenterC11C52
FrattiniC1G
Fitting, socleC5×C11C5
LCSG ▷ C11
UCSC1 ◁ C5

16 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:

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

Conjugacy classes & character table

35 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽11), D5×C11⋊C5, C5⋊AGL(1,𝔽11), …
maximal normal subgroup ofC5×AGL(1,𝔽11), D5×C11⋊C5, C5⋊AGL(1,𝔽11), …
maximal quotient ofC2×C5×C11⋊C5, C3×C5×C11⋊C5, C25×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(275, 3);