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Cayley diagram

D101 #6068

order202
isoclinismisoclinic class of D101
automorphismAut(G) = AGL(1,𝔽101) (order 10100) · Inn(G) = G · Out(G) = C2×C25
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD101
unambiguous semidirect productC101⋊C2

Splittings

Fitting, socle, derived, SylowC101 ⋊ C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC101C2
LCSG ▷ C101
UCSC1

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 101
transitive degreeμt(G) = 101

A minimal faithful permutation representation — 2 generators on 101 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(2,101)(3,100)(4,99)(5,98)(6,97)(7,96)(8,95)(9,94)(10,93)(11,92)(12,91)(13,90)(14,89)(15,88)(16,87)(17,86)(18,85)(19,84)(20,83)(21,82)(22,81)(23,80)(24,79)(25,78)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Polycyclic presentation:

2,101|b^a=b^100

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#87938, C2×D101, C3×D101, …
maximal normal subgroup of#87938, C2×D101, C3×D101, …
maximal quotient ofDic101, C2×D101, C3×D101, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(202, 1);