Finite Group Databasebeta

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Cayley diagram

C5×#683 #87790

order400
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#683

Splittings

SylowC52 ⋊ C4⋊C4

Subgroups

subgroupG/H
centerC22×C5C2×D5
commutatorC2×C5C2×C4×C5
FrattiniC22C2×C5×D5
FittingC2×C4×C52C2
socle, prime radicalC22×C52C22
cosocleC22×C5C22×C5
hypercenterC2×C4×C5D5
hypocenterC5C5×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C5 ◁ C2×C4×C5

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2,3,4,5)(6,7,9,10,8)(11,12,13,14)(16,18);(7,8)(9,10)(15,16,17,18)

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716954, #11716955, #11716956, …
maximal normal subgroup of#11716954, #11716955, #11716956, …
maximal quotient ofC5×#3939, C5×#3940, C5×#3946, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 84);