Finite Group Databasebeta

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Cayley diagram

D208 #88039

order416
isoclinismisoclinic class of D208
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD208

Splittings

FittingC13×C16 ⋊ C2
SylowC13 ⋊ D16

Subgroups

subgroupG/H
centerC2D104
commutator, cosocleC8×C13C22
FrattiniC8C2×D13
FittingC13×C16C2
socleC2×C13D8
hypercenterC16D13
hypocenterC13D16
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 208

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

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

Polycyclic presentation:

2^5,13|b^2=cd,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^12

Conjugacy classes & character table

107 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD416, #11718041, #11718111, …
maximal normal subgroup ofD416, #11718041, #11718111, …
maximal quotient ofD416, #11718041, Dic208, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 6);