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C2×D8029 #44545812

order32116
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16058
direct productC2×D8029
unambiguous semidirect product(C2×C7)⋊D1147
unambiguous semidirect product(C2×C31)⋊D259
unambiguous semidirect product(C2×C37)⋊D217

Splittings

Fitting, socleC2×C7×C31×C37 ⋊ C2
derived, HallC7×C31×C37 ⋊ C22
HallC31×C37 ⋊ C2×D7
HallC7×C37 ⋊ C2×D31
HallC7×C31 ⋊ C2×D37
SylowC37 ⋊ C2×D217
SylowC31 ⋊ C2×D259
SylowC7 ⋊ C2×D1147

Subgroups

subgroupG/H
center, hypercenterC2D8029
commutator, cosocle, hypocenterC7×C31×C37C22
FrattiniC1G
Fitting, socleC2×C7×C31×C37C2
LCSG ▷ C7×C31×C37
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 77
transitive degreeμt(G) = 16058

A minimal faithful permutation representation — 2 generators on 77 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);(4,9)(5,8)(6,7)(11,40)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60)

Conjugacy classes & character table

8032 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD32116
maximal normal subgroup ofD32116
maximal quotient ofDic16058, D32116

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32116, 27);