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C2×D8177 #45658481

order32708
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16354
direct productC2×D8177
unambiguous semidirect product(C2×C13)⋊D629
unambiguous semidirect product(C2×C17)⋊D481
unambiguous semidirect product(C2×C37)⋊D221

Splittings

Fitting, socleC2×C13×C17×C37 ⋊ C2
derived, HallC13×C17×C37 ⋊ C22
HallC17×C37 ⋊ C2×D13
HallC13×C37 ⋊ C2×D17
HallC13×C17 ⋊ C2×D37
SylowC37 ⋊ C2×D221
SylowC17 ⋊ C2×D481
SylowC13 ⋊ C2×D629

Subgroups

subgroupG/H
center, hypercenterC2D8177
commutator, cosocle, hypocenterC13×C17×C37C22
FrattiniC1G
Fitting, socleC2×C13×C17×C37C2
LCSG ▷ C13×C17×C37
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 69
transitive degreeμt(G) = 16354

A minimal faithful permutation representation — 2 generators on 69 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);(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Conjugacy classes & character table

8180 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD32708
maximal normal subgroup ofD32708
maximal quotient ofDic16354, D32708

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32708, 51);