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C2×D4095 #30655186

order16380
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD8190
direct productC2×D4095
unambiguous semidirect product(C2×C5)⋊D819
unambiguous semidirect product(C2×C7)⋊D585
unambiguous semidirect product(C2×C9)⋊D455
unambiguous semidirect product(C2×C13)⋊D315

Splittings

FittingC2×C5×C7×C9×C13 ⋊ C2
derived, HallC5×C7×C9×C13 ⋊ C22
HallC7×C9×C13 ⋊ C2×D5
HallC5×C9×C13 ⋊ C2×D7
HallC5×C7×C13 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D13
HallC9×C13 ⋊ C2×D35
HallC7×C13 ⋊ C2×D45
HallC5×C13 ⋊ C2×D63
HallC7×C9 ⋊ C2×D65
HallC5×C9 ⋊ C2×D91
HallC5×C7 ⋊ C2×D117
SylowC13 ⋊ C2×D315
SylowC9 ⋊ C2×D455
SylowC7 ⋊ C2×D585
SylowC5 ⋊ C2×D819

Subgroups

subgroupG/H
center, hypercenterC2D4095
commutator, cosocle, hypocenterC5×C7×C9×C13C22
FrattiniC3C2×D1365
FittingC2×C5×C7×C9×C13C2
socleC2×C3×C5×C7×C13D3
LCSG ▷ C5×C7×C9×C13
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 8190

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);(4,11)(5,10)(6,9)(7,8)(13,16)(14,15)(18,23)(19,22)(20,21)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

Conjugacy classes & character table

4098 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD16380, C2×D12285
maximal normal subgroup ofD16380
maximal quotient ofDic8190, D16380, C2×D12285

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 236);