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C2×D3477 #28358103

order13908
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD6954
direct productC2×D3477
unambiguous semidirect product(C2×C3)⋊D1159
unambiguous semidirect product(C2×C19)⋊D183
unambiguous semidirect product(C2×C61)⋊D57

Splittings

Fitting, socleC2×C3×C19×C61 ⋊ C2
derived, HallC3×C19×C61 ⋊ C22
HallC19×C61 ⋊ C2×D3
HallC3×C61 ⋊ C2×D19
SylowC61 ⋊ C2×D57
HallC3×C19 ⋊ C2×D61
SylowC19 ⋊ C2×D183
SylowC3 ⋊ C2×D1159

Subgroups

subgroupG/H
center, hypercenterC2D3477
commutator, cosocle, hypocenterC3×C19×C61C22
FrattiniC1G
Fitting, socleC2×C3×C19×C61C2
LCSG ▷ C3×C19×C61
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 85
transitive degreeμt(G) = 6954

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

Conjugacy classes & character table

3480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD13908
maximal normal subgroup ofD13908
maximal quotient ofD13908, Dic6954

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13908, 70);