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C5×#63725 #13085377

order1440
isoclinismisoclinic class of AGL(1,𝔽9)
automorphism?
homologyAbelianization (H1) = C5×C32 · Schur multiplier (H2) = C1

Aliases

direct productC5×#63725

Splittings

derived, SylowC32 ⋊ C5×C32
HallC32×C5 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC4×C5AGL(1,𝔽9)
commutator, hypocenterC32C5×C32
FrattiniC4C5×AGL(1,𝔽9)
FittingC32×C4×C5C8
socle, prime radicalC2×C32×C5C16
cosocle#3708C2×C5
LCSG ▷ C32
UCSC1 ◁ C4×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2,3,4,5)(7,8,9,12,10,13,14,11)(15,16,17,21,18,22,25,31,19,23,26,32,28,34,37,41,20,24,27,33,29,35,38,42,30,36,39,43,40,44,45,46);(6,9,14)(7,12,8)(10,13,11)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1694);