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C5×#4520 #11746219

order960
isoclinismisoclinic class of #4519
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#4520

Splittings

HallC3×C5 ⋊ SD64
SylowC3 ⋊ C5×SD64

Subgroups

subgroupG/H
centerC2×C5#826
commutator, cosocleC3×C16C22×C5
FrattiniC16C2×C5×D3
Fitting, prime radicalC3×C5×D16C2
socleC2×C3×C5D16
hypercenterC5×D16D3
hypocenterC3C5×SD64
LCSG ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×C16 ◁ C5×D16

64 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)(18,36)(19,30)(22,39)(23,31)(24,28)(26,34)(27,29)(32,40)(33,35)(37,38);(7,8)(9,10,14,19)(11,15,23,30)(12,24,26,40)(13,27,25,18)(16,31,33,20)(17,34,35,21)(22,36,37,29)(28,39,32,38)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×SD64, C2×C5×#4520, D5×#4520, …
maximal normal subgroup ofC5×D3×SD64, C2×C5×#4520, D5×#4520, …
maximal quotient ofC5×#67824, C5×#67578, C5×#67576, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 414);