Finite Group Databasebeta

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Cayley diagram

C2×C4×C5×D5 #87888

order400
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×C5×D5

Splittings

FittingC2×C4×C52 ⋊ C2
derivedC5 ⋊ C22×C4×C5
SylowC52 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4×C5D5
commutator, hypocenterC5C22×C4×C5
FrattiniC2C22×C5×D5
FittingC2×C4×C52C2
socleC22×C52C22
prime radicalC22×C5×D5C2
cosocleC2×C5C23×C5
LCSG ▷ C5
UCSC1 ◁ C2×C4×C5

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716597, C5×#3952, C5×#4003, …
maximal normal subgroup of#11716597, C5×#3952, C5×#4003, …
maximal quotient ofC4×C5×Dic10, C42×C5×D5, C5×#4018, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 182);