Finite Group Databasebeta

← Prev (#92541) Next (#92543) →

Cayley diagram

C2×C5×D25 #92542

order500
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D25

Splittings

FittingC2×C5×C25 ⋊ C2
derivedC25 ⋊ C22×C5
SylowC5×C25 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C5D25
commutator, cosocle, hypocenterC25C22×C5
FrattiniC5C2×C5×D5
FittingC2×C5×C25C2
socleC2×C52D5
LCSG ▷ C25
UCSC1 ◁ C2×C5

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 100

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×D25, #11758653, #11758655, …
maximal normal subgroup ofDic5×D25, #11758653, #11758655, …
maximal quotient ofC5×Dic50, C4×C5×D25, C5×D100, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(500, 28);