Finite Group Databasebeta

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C5×#63540 #13084629

order1440
isoclinismisoclinic class of #157
automorphism?
homologyAbelianization (H1) = C5×C32 · Schur multiplier (H2) = C3

Aliases

direct productC5×#63540

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C8#157
commutator, hypocenterC32C5×C32
FrattiniC8C5×#157
FittingC32×C5×C8C4
socle, prime radicalC2×C32×C5C16
cosocleC3⋊(C3⋊C16)C2×C5
LCSG ▷ C32
UCSC1 ◁ C5×C8

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 946);