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C2×D3657 #28410677

order14628
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7314
direct productC2×D3657
unambiguous semidirect product(C2×C3)⋊D1219
unambiguous semidirect product(C2×C23)⋊D159
unambiguous semidirect product(C2×C53)⋊D69

Splittings

Fitting, socleC2×C3×C23×C53 ⋊ C2
derived, HallC3×C23×C53 ⋊ C22
HallC23×C53 ⋊ C2×D3
HallC3×C53 ⋊ C2×D23
HallC3×C23 ⋊ C2×D53
SylowC53 ⋊ C2×D69
SylowC23 ⋊ C2×D159
SylowC3 ⋊ C2×D1219

Subgroups

subgroupG/H
center, hypercenterC2D3657
commutator, cosocle, hypocenterC3×C23×C53C22
FrattiniC1G
Fitting, socleC2×C3×C23×C53C2
LCSG ▷ C3×C23×C53
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 81
transitive degreeμt(G) = 7314

A minimal faithful permutation representation — 2 generators on 81 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)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81);(4,5)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(30,81)(31,80)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,73)(39,72)(40,71)(41,70)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)

Conjugacy classes & character table

3660 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD14628
maximal normal subgroup ofD14628
maximal quotient ofD14628, Dic7314

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14628, 22);