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C2×D2915 #26042940

order11660
automorphismAut(G) order 12126400
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD5830
direct productC2×D2915
unambiguous semidirect product(C2×C5)⋊D583
unambiguous semidirect product(C2×C11)⋊D265
unambiguous semidirect product(C2×C53)⋊D55

Splittings

Fitting, socleC2×C5×C11×C53 ⋊ C2
derived, HallC5×C11×C53 ⋊ C22
HallC11×C53 ⋊ C2×D5
HallC5×C53 ⋊ C2×D11
HallC5×C11 ⋊ C2×D53
SylowC53 ⋊ C2×D55
SylowC11 ⋊ C2×D265
SylowC5 ⋊ C2×D583

Subgroups

subgroupG/H
center, hypercenterC2D2915
commutator, cosocle, hypocenterC5×C11×C53C22
FrattiniC1G
Fitting, socleC2×C5×C11×C53C2
LCSG ▷ C5×C11×C53
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 71
transitive degreeμt(G) = 5830

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);(4,7)(5,6)(9,18)(10,17)(11,16)(12,15)(13,14)(20,71)(21,70)(22,69)(23,68)(24,67)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)

Conjugacy classes & character table

2918 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×D2915, C2×C3×D2915, C2×D8745, …
maximal normal subgroup ofC2×C3×D2915, D11660
maximal quotient ofD3×D2915, C2×C3×D2915, C2×D8745, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11660, 40);