Finite Group Databasebeta

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C32×#3994 #13086246

order1440
isoclinismisoclinic class of #3993
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×#3994

Splittings

FittingC32×C5×C8 ⋊ C4
HallC32×C5 ⋊ #107
SylowC5 ⋊ C32×#107

Subgroups

subgroupG/H
centerC2×C32C4⋊AGL(1,𝔽5)
commutatorC4×C5C2×C32×C4
FrattiniC4C2×C32×AGL(1,𝔽5)
FittingC32×C5×C8C4
socleC2×C32×C5C4⋊C4
prime radicalC2×C32×D5D4
cosocleC4×D5C22×C32
hypercenterC32×C8AGL(1,𝔽5)
hypocenterC5C32×#107
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C32 ◁ C32×C4 ◁ C32×C8

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 360

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

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

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2563);