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Cayley diagram

D155 #64582

order310
isoclinismisoclinic class of D155
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD155
unambiguous semidirect productC5⋊D31
unambiguous semidirect productC31⋊D5

Splittings

Fitting, socle, derived, HallC5×C31 ⋊ C2
SylowC31 ⋊ D5
SylowC5 ⋊ D31

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C31C2
LCSG ▷ C5×C31
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 155

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

Polycyclic presentation:

2,5,31|b^a=b^4,c^a=c^30

Conjugacy classes & character table

79 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×D31, C2×D155, C5⋊(D31⋊C3), …
maximal normal subgroup ofD5×D31, C2×D155, C5⋊(D31⋊C3), …
maximal quotient ofDic155, C2×D155, C3×D155, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(310, 5);