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D988 #14520356

order1976
automorphismAut(G) order 426816
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD988
unambiguous semidirect productC4⋊D247

Splittings

FittingC4×C13×C19 ⋊ C2
HallC13×C19 ⋊ D4
SylowC19 ⋊ D52
SylowC13 ⋊ D76

Subgroups

subgroupG/H
center, FrattiniC2C2×D247
commutator, socle, cosocleC2×C13×C19C22
FittingC4×C13×C19C2
hypercenterC4D247
hypocenterC13×C19D4
LCSG ▷ C2×C13×C19 ▷ C13×C19
UCSC1 ◁ C2 ◁ C4

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 988

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);(2,4)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)

Polycyclic presentation:

2^3,13,19|b^2=c,b^a=bc,d^a=d^12,e^a=e^18

Conjugacy classes & character table

497 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD2964, D1976, D4940, …
maximal normal subgroup ofD1976
maximal quotient ofD2964, D1976, D4940, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1976, 26);