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Cayley diagram

D5×Dic5 #6035

order200
isoclinismisoclinic class of D52
automorphismAut(G) = C22×AGL(1,𝔽5)2 (order 1600) · Inn(G) = D52 · Out(G) = C24
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productD5×Dic5

Splittings

derived, SylowC52 ⋊ C2×C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D52
commutator, hypocenterC52C2×C4
Fitting, socle, cosocleC2×C52C22
prime radicalC2×C5×D5C2
LCSG ▷ C52
UCSC1 ◁ C2

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 14
transitive degreeμt(G) = 40

A minimal faithful permutation representation — 2 generators on 14 points:

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

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×AGL(1,𝔽5), #87825, D5×#170, …
maximal normal subgroup ofDic5×AGL(1,𝔽5), #87825, D5×#170, …
maximal quotient ofD5×#168, #87768, Dic52, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 22);