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C2×D3913 #30627786

order15652
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7826
direct productC2×D3913
unambiguous semidirect product(C2×C7)⋊D559
unambiguous semidirect product(C2×C13)⋊D301
unambiguous semidirect product(C2×C43)⋊D91

Splittings

Fitting, socleC2×C7×C13×C43 ⋊ C2
derived, HallC7×C13×C43 ⋊ C22
HallC13×C43 ⋊ C2×D7
HallC7×C43 ⋊ C2×D13
HallC7×C13 ⋊ C2×D43
SylowC43 ⋊ C2×D91
SylowC13 ⋊ C2×D301
SylowC7 ⋊ C2×D559

Subgroups

subgroupG/H
center, hypercenterC2D3913
commutator, cosocle, hypocenterC7×C13×C43C22
FrattiniC1G
Fitting, socleC2×C7×C13×C43C2
LCSG ▷ C7×C13×C43
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 65
transitive degreeμt(G) = 7826

A minimal faithful permutation representation — 2 generators on 65 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);(4,9)(5,8)(6,7)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(24,65)(25,64)(26,63)(27,62)(28,61)(29,60)(30,59)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)

Conjugacy classes & character table

3916 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD15652
maximal normal subgroup ofD15652
maximal quotient ofDic7826, D15652

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15652, 32);