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Cayley diagram

C32×C5×D5 #90661

order450
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×D5
unambiguous semidirect productC5⋊(C2×C32×C5)

Splittings

Fitting, socle, HallC32×C52 ⋊ C2
derivedC5 ⋊ C2×C32×C5
SylowC52 ⋊ C2×C32

Subgroups

subgroupG/H
center, hypercenterC32×C5D5
commutator, cosocle, hypocenterC5C2×C32×C5
FrattiniC1G
Fitting, socleC32×C52C2
LCSG ▷ C5
UCSC1 ◁ C32×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 90

A minimal faithful permutation representation — 2 generators on 16 points:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×C5×AGL(1,𝔽5), C32×#1042, C3×C5×ΓL(1,𝔽16), …
maximal normal subgroup ofC32×C5×AGL(1,𝔽5), C32×#1042, C3×C5×ΓL(1,𝔽16), …
maximal quotient ofC32×C5×Dic5, C2×C32×C5×D5, C3×C5×C9×D5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 26);