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C2×D9139 #49143191

order36556
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18278
direct productC2×D9139
unambiguous semidirect product(C2×C13)⋊D703
unambiguous semidirect product(C2×C19)⋊D481
unambiguous semidirect product(C2×C37)⋊D247

Splittings

Fitting, socleC2×C13×C19×C37 ⋊ C2
derived, HallC13×C19×C37 ⋊ C22
HallC19×C37 ⋊ C2×D13
HallC13×C37 ⋊ C2×D19
HallC13×C19 ⋊ C2×D37
SylowC37 ⋊ C2×D247
SylowC19 ⋊ C2×D481
SylowC13 ⋊ C2×D703

Subgroups

subgroupG/H
center, hypercenterC2D9139
commutator, cosocle, hypocenterC13×C19×C37C22
FrattiniC1G
Fitting, socleC2×C13×C19×C37C2
LCSG ▷ C13×C19×C37
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 71
transitive degreeμt(G) = 18278

A minimal faithful permutation representation — 2 generators on 71 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)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71);(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(36,71)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,64)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)

Conjugacy classes & character table

9142 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36556, 35);