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C5×C22⋊#261 #11760190

order1040
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×C22⋊#261
unambiguous semidirect productC22⋊(C5×#261)
unambiguous semidirect product(C2×#261)⋊(C2×C5)

Splittings

FittingC22×C5×C13 ⋊ C4
HallC5×C13 ⋊ C22⋊C4
SylowC13 ⋊ C5×C22⋊C4

Subgroups

subgroupG/H
centerC2×C5C2×#261
commutatorC2×C13C2×C4×C5
FrattiniC2C2×C5×#261
FittingC22×C5×C13C4
socleC2×C5×C13C2×C4
prime radicalC22×C5×D13C2
cosocleC2×D13C22×C5
hypercenterC22×C5#261
hypocenterC13C5×C22⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C5 ◁ C22×C5

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 260

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3,4,5)(6,7,10,13,17,11,15,16,8,12,18,14,9)(20,22);(7,8,9,11)(10,13,14,18)(12,16,17,15)(19,20)(21,22)

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1040, 119);