Finite Group Databasebeta

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Cayley diagram

C2×C4×C5⋊D5 #87898

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

Aliases

direct productC2×C4×C5⋊D5

Splittings

FittingC2×C4×C52 ⋊ C2
derived, SylowC52 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4C5⋊D5
commutator, hypocenterC52C22×C4
FrattiniC2C22×C5⋊D5
FittingC2×C4×C52C2
socleC22×C52C22
prime radicalC22×C5⋊D5C2
cosocleC2×C52C23
LCSG ▷ C52
UCSC1 ◁ C2×C4

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 200

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

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716598, #11716687, #11716871, …
maximal normal subgroup of#11716598, #11716687, #11716871, …
maximal quotient ofC4×#6045, C42×C5⋊D5, #11717192, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 192);