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C5×#4519 #11746218

order960
isoclinismisoclinic class of #4519
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#4519

Splittings

FittingC3×C5×D16 ⋊ C2
HallC3×C5 ⋊ D32
SylowC3 ⋊ C5×D32

Subgroups

subgroupG/H
centerC2×C5#826
commutator, cosocleC3×C16C22×C5
FrattiniC16C2×C5×D3
FittingC3×C5×D16C2
socleC2×C3×C5D16
hypercenterC5×D16D3
hypocenterC3C5×D32
LCSG ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×C16 ◁ C5×D16

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×D32, C2×C5×#4519, D5×#4519, …
maximal normal subgroup ofC5×D3×D32, C2×C5×#4519, D5×#4519, …
maximal quotient ofC5×#67577, C5×#67824, C5×#67575, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 413);