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Cayley diagram

D5×C47 #90882

order470
isoclinismisoclinic class of D5
automorphismAut(G) = C2×AGL(1,𝔽5)×C23 (order 920) · Inn(G) = D5 · Out(G) = C22×C23
homologyAbelianization (H1) = C2×C47 · Schur multiplier (H2) = C1

Aliases

direct productD5×C47
unambiguous semidirect productC5⋊(C2×C47)

Splittings

Fitting, socle, HallC5×C47 ⋊ C2
derived, SylowC5 ⋊ C2×C47

Subgroups

subgroupG/H
center, hypercenterC47D5
commutator, cosocle, hypocenterC5C2×C47
FrattiniC1G
Fitting, socleC5×C47C2
LCSG ▷ C5
UCSC1 ◁ C47

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 235

A minimal faithful permutation representation — 2 generators on 52 points:

(2,3)(4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52);(1,2,4,5,3)

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C47, C47⋊AGL(1,𝔽5), D5×D47, …
maximal normal subgroup ofAGL(1,𝔽5)×C47, C47⋊AGL(1,𝔽5), D5×D47, …
maximal quotient ofDic5×C47, C2×D5×C47, C3×D5×C47, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(470, 1);