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C2×D3621 #28407985

order14484
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7242
direct productC2×D3621
unambiguous semidirect product(C2×C3)⋊D1207
unambiguous semidirect product(C2×C17)⋊D213
unambiguous semidirect product(C2×C71)⋊D51

Splittings

Fitting, socleC2×C3×C17×C71 ⋊ C2
derived, HallC3×C17×C71 ⋊ C22
HallC17×C71 ⋊ C2×D3
HallC3×C71 ⋊ C2×D17
SylowC71 ⋊ C2×D51
HallC3×C17 ⋊ C2×D71
SylowC17 ⋊ C2×D213
SylowC3 ⋊ C2×D1207

Subgroups

subgroupG/H
center, hypercenterC2D3621
commutator, cosocle, hypocenterC3×C17×C71C22
FrattiniC1G
Fitting, socleC2×C3×C17×C71C2
LCSG ▷ C3×C17×C71
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 93
transitive degreeμt(G) = 7242

A minimal faithful permutation representation — 2 generators on 93 points:

(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(4,5)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(24,93)(25,92)(26,91)(27,90)(28,89)(29,88)(30,87)(31,86)(32,85)(33,84)(34,83)(35,82)(36,81)(37,80)(38,79)(39,78)(40,77)(41,76)(42,75)(43,74)(44,73)(45,72)(46,71)(47,70)(48,69)(49,68)(50,67)(51,66)(52,65)(53,64)(54,63)(55,62)(56,61)(57,60)(58,59)

Conjugacy classes & character table

3624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD14484
maximal normal subgroup ofD14484
maximal quotient ofD14484, Dic7242

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14484, 22);