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Cayley diagram

D29 #297

order58
isoclinismisoclinic class of D29
automorphismAut(G) = AGL(1,𝔽29) (order 812) · Inn(G) = G · Out(G) = C2×C7
holomorphG ⋊ Aut(G) = #72257984
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD29
unambiguous semidirect productC29⋊C2

Splittings

Fitting, socle, derived, SylowC29 ⋊ C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC29C2
LCSG ▷ C29
UCSC1

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2,29|b^a=b^28

Conjugacy classes & character table

16 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#1181, C2×D29, C3×D29, …
maximal normal subgroup of#1181, C2×D29, C3×D29, …
maximal quotient ofDic29, C2×D29, C3×D29, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(58, 1);