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C2×D7665 #44501473

order30660
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15330
direct productC2×D7665
unambiguous semidirect product(C2×C3)⋊D2555
unambiguous semidirect product(C2×C5)⋊D1533
unambiguous semidirect product(C2×C7)⋊D1095
unambiguous semidirect product(C2×C73)⋊D105

Splittings

Fitting, socleC2×C3×C5×C7×C73 ⋊ C2
derived, HallC3×C5×C7×C73 ⋊ C22
HallC5×C7×C73 ⋊ C2×D3
HallC3×C7×C73 ⋊ C2×D5
HallC3×C5×C73 ⋊ C2×D7
HallC7×C73 ⋊ C2×D15
HallC5×C73 ⋊ C2×D21
HallC3×C73 ⋊ C2×D35
HallC3×C5×C7 ⋊ C2×D73
SylowC73 ⋊ C2×D105
HallC5×C7 ⋊ C2×D219
HallC3×C7 ⋊ C2×D365
HallC3×C5 ⋊ C2×D511
SylowC7 ⋊ C2×D1095
SylowC5 ⋊ C2×D1533
SylowC3 ⋊ C2×D2555

Subgroups

subgroupG/H
center, hypercenterC2D7665
commutator, cosocle, hypocenterC3×C5×C7×C73C22
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C73C2
LCSG ▷ C3×C5×C7×C73
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 90
transitive degreeμt(G) = 15330

A minimal faithful permutation representation — 2 generators on 90 points:

(1,2)(3,4,5)(6,7,8,9,10)(11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90);(4,5)(7,10)(8,9)(12,17)(13,16)(14,15)(19,90)(20,89)(21,88)(22,87)(23,86)(24,85)(25,84)(26,83)(27,82)(28,81)(29,80)(30,79)(31,78)(32,77)(33,76)(34,75)(35,74)(36,73)(37,72)(38,71)(39,70)(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

7668 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD30660
maximal normal subgroup ofD30660
maximal quotient ofDic15330, D30660

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 236);