Finite Group Databasebeta

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Cayley diagram

C22×C5×Dic5 #87895

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

Aliases

direct productC22×C5×Dic5

Splittings

derivedC5 ⋊ C22×C4×C5
SylowC52 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC23×C5D5
commutator, hypocenterC5C22×C4×C5
FrattiniC2C22×C5×D5
Fitting, socle, prime radicalC23×C52C2
cosocleC2×C5C23×C5
LCSG ▷ C5
UCSC1 ◁ C23×C5

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 18 points:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716620, C5×#3963, C5×C22⋊#170, …
maximal normal subgroup of#11716620, C5×#3963, C5×C22⋊#170, …
maximal quotient ofC22×C5×#168, C2×C5×#681, C2×C4×C5×Dic5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 189);