Finite Group Databasebeta

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Cayley diagram

C22×Dic25 #87749

order400
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×Dic25

Splittings

derived, SylowC25 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC23D25
commutator, hypocenterC25C22×C4
FrattiniC2×C5C22×D5
FittingC23×C25C2
socle, prime radicalC23×C5D5
cosocleC2×C25C23
LCSG ▷ C25
UCSC1 ◁ C23

81 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 400

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2)(3,4)(5,6,7,8)(10,12)(11,15)(13,18)(14,21)(16,24)(17,23)(19,20)(22,28)(25,29)(26,30)(27,32)(31,33);(3,4)(9,23,33,26,12,15,29,27,18,21,24,22,20,19,28,16,14,13,32,25,11,10,30,31,17);(1,2)

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716379, C22⋊#6016, #11716439, …
maximal normal subgroup of#11716379, C22⋊#6016, #11716439, …
maximal quotient ofC22×#6014, C2×#87716, C2×C4×Dic25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 43);