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D1085 #14524246

order2170
isoclinismisoclinic class of D1085
automorphismAut(G) order 781200
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD1085
unambiguous semidirect productC5⋊D217
unambiguous semidirect productC7⋊D155
unambiguous semidirect productC31⋊D35

Splittings

Fitting, socle, derived, HallC5×C7×C31 ⋊ C2
HallC7×C31 ⋊ D5
HallC5×C31 ⋊ D7
HallC5×C7 ⋊ D31
SylowC31 ⋊ D35
SylowC7 ⋊ D155
SylowC5 ⋊ D217

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C31C2
LCSG ▷ C5×C7×C31
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 1085

A minimal faithful permutation representation — 2 generators on 43 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);(2,5)(3,4)(7,12)(8,11)(9,10)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)

Polycyclic presentation:

2,5,7,31|b^a=b^4,c^a=c^6,d^a=d^30

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD31×D35, D7×D155, D5×D217, …
maximal normal subgroup ofD31×D35, D7×D155, D5×D217, …
maximal quotient ofDic1085, C2×D1085, D5425, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2170, 9);