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Cayley diagram

C2×D29 #1182

order116
isoclinismisoclinic class of D29
automorphismAut(G) = C2×AGL(1,𝔽29) (order 1624) · Inn(G) = D29 · Out(G) = C22×C7
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD58
direct productC2×D29
unambiguous semidirect productC29⋊C22
unambiguous semidirect product(C2×C29)⋊C2

Splittings

Fitting, socleC2×C29 ⋊ C2
derived, SylowC29 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2D29
commutator, cosocle, hypocenterC29C22
FrattiniC1G
Fitting, socleC2×C29C2
LCSG ▷ C29
UCSC1 ◁ C2

10 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 58

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D29, D116, C22⋊D29, …
maximal normal subgroup ofC4×D29, D116, C22⋊D29, …
maximal quotient ofDic58, C4×D29, D116, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(116, 4);