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Cayley diagram

D203 #87961

order406
isoclinismisoclinic class of D203
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD203
unambiguous semidirect productC7⋊D29
unambiguous semidirect productC29⋊D7

Splittings

Fitting, socle, derived, HallC7×C29 ⋊ C2
SylowC29 ⋊ D7
SylowC7 ⋊ D29

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C29C2
LCSG ▷ C7×C29
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 203

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36);(2,7)(3,6)(4,5)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)

Polycyclic presentation:

2,7,29|b^a=b^6,c^a=c^28

Conjugacy classes & character table

103 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×D29, C2×D203, ΓL(1,𝔽8)⋊D29, …
maximal normal subgroup ofD7×D29, C2×D203, ΓL(1,𝔽8)⋊D29, …
maximal quotient ofDic203, C2×D203, C3×D203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(406, 5);