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Cayley diagram

D29⋊C7 #87957

order406
isoclinismisoclinic class of D29⋊C7
automorphismAut(G) = AGL(1,𝔽29) (order 812) · Inn(G) = G · Out(G) = C2
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productD29⋊C7
unambiguous semidirect product(C29⋊C7)⋊C2

Splittings

Fitting, socle, derived, SylowC29 ⋊ C2×C7
HallC29⋊C7 ⋊ C2
HallD29 ⋊ C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC29C2×C7
LCSG ▷ C29
UCSC1

8 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:

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

Polycyclic presentation:

2,7,29|c^a=c^28,c^b=c^16

Conjugacy classes & character table

16 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽29), C2×D29⋊C7, C3×D29⋊C7, …
maximal normal subgroup ofAGL(1,𝔽29), C2×D29⋊C7, C3×D29⋊C7, …
maximal quotient ofDic29⋊C7, C2×D29⋊C7, C3×D29⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(406, 1);