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C2×D3819 #29504172

order15276
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7638
direct productC2×D3819
unambiguous semidirect product(C2×C3)⋊D1273
unambiguous semidirect product(C2×C19)⋊D201
unambiguous semidirect product(C2×C67)⋊D57

Splittings

Fitting, socleC2×C3×C19×C67 ⋊ C2
derived, HallC3×C19×C67 ⋊ C22
HallC19×C67 ⋊ C2×D3
HallC3×C67 ⋊ C2×D19
SylowC67 ⋊ C2×D57
HallC3×C19 ⋊ C2×D67
SylowC19 ⋊ C2×D201
SylowC3 ⋊ C2×D1273

Subgroups

subgroupG/H
center, hypercenterC2D3819
commutator, cosocle, hypocenterC3×C19×C67C22
FrattiniC1G
Fitting, socleC2×C3×C19×C67C2
LCSG ▷ C3×C19×C67
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 91
transitive degreeμt(G) = 7638

A minimal faithful permutation representation — 2 generators on 91 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);(4,5)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(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

3822 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD15276
maximal normal subgroup ofD15276
maximal quotient ofD15276, Dic7638

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15276, 58);