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Cayley diagram

C4×D25 #6018

order200
isoclinismisoclinic class of D25
automorphismAut(G) = C22×AGL(1,ℤ/25) (order 2000) · Inn(G) = D25 · Out(G) = C23×C5
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×D25

Splittings

FittingC4×C25 ⋊ C2
derived, SylowC25 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4D25
commutator, hypocenterC25C2×C4
Frattini, socleC2×C5C2×D5
FittingC4×C25C2
prime radicalC2×D25C2
cosocleC2×C25C22
LCSG ▷ C25
UCSC1 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 100

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×D25, #87712, D25⋊C8, …
maximal normal subgroup ofC8×D25, #87712, D25⋊C8, …
maximal quotient ofC8×D25, #87712, C4×Dic25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 5);