Finite Group Databasebeta

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C5×#63422 #13083940

order1440
isoclinismisoclinic class of #3688
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#63422

Splittings

derivedQ8⋊C9 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5(C22⋊C9)⋊C2
commutator, hypocenterQ8⋊C9C4×C5
FrattiniC3×C4C5×S4
Fitting, prime radicalC3×C5×#41D3
socleC2×C3×C5SL(2,ℤ/4)
cosocle#41⋊C9C2×C5
LCSG ▷ Q8⋊C9
UCSC1 ◁ C4×C5

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 360

A minimal faithful permutation representation — 2 generators on 38 points:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 257);