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D481 #11757204

order962
isoclinismisoclinic class of D481
automorphismAut(G) order 207792
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD481
unambiguous semidirect productC13⋊D37
unambiguous semidirect productC37⋊D13

Splittings

Fitting, socle, derived, HallC13×C37 ⋊ C2
SylowC37 ⋊ D13
SylowC13 ⋊ D37

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C37C2
LCSG ▷ C13×C37
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 481

A minimal faithful permutation representation — 2 generators on 50 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)

Polycyclic presentation:

2,13,37|b^a=b^12,c^a=c^36

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14515320, #14515321, D13×D37, …
maximal normal subgroup of#14515320, #14515321, D13×D37, …
maximal quotient ofDic481, C2×D481, C3×D481, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(962, 3);