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C2×D9269 #49150523

order37076
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18538
direct productC2×D9269
unambiguous semidirect product(C2×C13)⋊D713
unambiguous semidirect product(C2×C23)⋊D403
unambiguous semidirect product(C2×C31)⋊D299

Splittings

Fitting, socleC2×C13×C23×C31 ⋊ C2
derived, HallC13×C23×C31 ⋊ C22
HallC23×C31 ⋊ C2×D13
HallC13×C31 ⋊ C2×D23
HallC13×C23 ⋊ C2×D31
SylowC31 ⋊ C2×D299
SylowC23 ⋊ C2×D403
SylowC13 ⋊ C2×D713

Subgroups

subgroupG/H
center, hypercenterC2D9269
commutator, cosocle, hypocenterC13×C23×C31C22
FrattiniC1G
Fitting, socleC2×C13×C23×C31C2
LCSG ▷ C13×C23×C31
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 69
transitive degreeμt(G) = 18538

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

Conjugacy classes & character table

9272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37076, 27);