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C3×C11⋊AGL(1,𝔽5) #10620352

order660
isoclinismisoclinic class of C11⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(C3×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C11 ⋊ C4
derived, HallC5×C11 ⋊ C3×C4
HallC3×C11 ⋊ AGL(1,𝔽5)
HallC3×C5 ⋊ Dic11
SylowC11 ⋊ C3×AGL(1,𝔽5)
SylowC5 ⋊ C3×Dic11

Subgroups

subgroupG/H
center, hypercenterC3C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C4
FrattiniC1G
Fitting, socleC3×C5×C11C4
prime radicalC3×D5×C11C2
cosocleD5×C11C2×C3
LCSG ▷ C5×C11
UCSC1 ◁ C3

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 165

A minimal faithful permutation representation — 2 generators on 19 points:

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

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×D11, D3×C11⋊AGL(1,𝔽5), ΓL(1,𝔽16)⋊D11, …
maximal normal subgroup ofC3×AGL(1,𝔽5)×D11, D3×C11⋊AGL(1,𝔽5), ΓL(1,𝔽16)⋊D11, …
maximal quotient ofC3×C11⋊#170, C2×C3×C11⋊AGL(1,𝔽5), C9×C11⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(660, 22);