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C2×D3575 #28384674

order14300
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7150
direct productC2×D3575
unambiguous semidirect product(C2×C11)⋊D325
unambiguous semidirect product(C2×C13)⋊D275
unambiguous semidirect product(C2×C25)⋊D143

Splittings

FittingC2×C11×C13×C25 ⋊ C2
derived, HallC11×C13×C25 ⋊ C22
HallC13×C25 ⋊ C2×D11
HallC11×C25 ⋊ C2×D13
HallC11×C13 ⋊ C2×D25
SylowC25 ⋊ C2×D143
SylowC13 ⋊ C2×D275
SylowC11 ⋊ C2×D325

Subgroups

subgroupG/H
center, hypercenterC2D3575
commutator, cosocle, hypocenterC11×C13×C25C22
FrattiniC5C2×D715
FittingC2×C11×C13×C25C2
socleC2×C5×C11×C13D5
LCSG ▷ C11×C13×C25
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 51
transitive degreeμt(G) = 7150

A minimal faithful permutation representation — 2 generators on 51 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);(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(29,38)(30,37)(31,36)(32,35)(33,34)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)

Conjugacy classes & character table

3578 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD14300
maximal normal subgroup ofD14300
maximal quotient ofD14300, Dic7150

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14300, 46);