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D295 #10596922

order590
isoclinismisoclinic class of D295
automorphismAut(G) order 68440
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD295
unambiguous semidirect productC5⋊D59
unambiguous semidirect productC59⋊D5

Splittings

Fitting, socle, derived, HallC5×C59 ⋊ C2
SylowC59 ⋊ D5
SylowC5 ⋊ D59

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C59C2
LCSG ▷ C5×C59
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 64
transitive degreeμt(G) = 295

A minimal faithful permutation representation — 2 generators on 64 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);(2,5)(3,4)(7,64)(8,63)(9,62)(10,61)(11,60)(12,59)(13,58)(14,57)(15,56)(16,55)(17,54)(18,53)(19,52)(20,51)(21,50)(22,49)(23,48)(24,47)(25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)

Polycyclic presentation:

2,5,59|b^a=b^4,c^a=c^58

Conjugacy classes & character table

149 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×D59, C2×D295, C3×D295, …
maximal normal subgroup ofD5×D59, C2×D295, C3×D295, …
maximal quotient ofDic295, C2×D295, C3×D295, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(590, 3);