Finite Group Databasebeta

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Cayley diagram

D145 #64402

order290
isoclinismisoclinic class of D145
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD145
unambiguous semidirect productC5⋊D29
unambiguous semidirect productC29⋊D5

Splittings

Fitting, socle, derived, HallC5×C29 ⋊ C2
SylowC29 ⋊ D5
SylowC5 ⋊ D29

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C29C2
LCSG ▷ C5×C29
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 145

A minimal faithful permutation representation — 2 generators on 34 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);(2,5)(3,4)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)

Polycyclic presentation:

2,5,29|b^a=b^4,c^a=c^28

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10596814, #10596815, D5×D29, …
maximal normal subgroup of#10596814, #10596815, D5×D29, …
maximal quotient ofDic145, C2×D145, C3×D145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(290, 3);