Finite Group Databasebeta

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Cayley diagram

C2×D5×Dic5 #87878

order400
isoclinismisoclinic class of D52
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×D5×Dic5

Splittings

derived, SylowC52 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22D52
commutator, hypocenterC52C22×C4
FrattiniC2C2×D52
Fitting, socleC22×C52C22
prime radicalC22×C5×D5C2
cosocleC2×C52C23
LCSG ▷ C52
UCSC1 ◁ C22

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×AGL(1,𝔽5))⋊Dic5, #11716753, #11716779, …
maximal normal subgroup of(C2×AGL(1,𝔽5))⋊Dic5, #11716753, #11716779, …
maximal quotient ofC2×D5×#168, D5×#681, #11716932, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 172);