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Cayley diagram

C2×D25 #1036

order100
isoclinismisoclinic class of D25
automorphismAut(G) = C2×AGL(1,ℤ/25) (order 1000) · Inn(G) = D25 · Out(G) = C22×C5
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD50
direct productC2×D25
unambiguous semidirect productC25⋊C22
unambiguous semidirect product(C2×C25)⋊C2

Splittings

FittingC2×C25 ⋊ C2
derived, SylowC25 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2D25
commutator, cosocle, hypocenterC25C22
FrattiniC5C2×D5
FittingC2×C25C2
socleC2×C5D5
LCSG ▷ C25
UCSC1 ◁ C2

15 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 50

A minimal faithful permutation representation — 2 generators on 27 points:

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

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D25, D100, C22⋊D25, …
maximal normal subgroup ofC4×D25, D100, C22⋊D25, …
maximal quotient ofDic50, C4×D25, D100, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(100, 4);