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C2×D5525 #36348454

order22100
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11050
direct productC2×D5525
unambiguous semidirect product(C2×C13)⋊D425
unambiguous semidirect product(C2×C17)⋊D325
unambiguous semidirect product(C2×C25)⋊D221

Splittings

FittingC2×C13×C17×C25 ⋊ C2
derived, HallC13×C17×C25 ⋊ C22
HallC17×C25 ⋊ C2×D13
HallC13×C25 ⋊ C2×D17
HallC13×C17 ⋊ C2×D25
SylowC25 ⋊ C2×D221
SylowC17 ⋊ C2×D325
SylowC13 ⋊ C2×D425

Subgroups

subgroupG/H
center, hypercenterC2D5525
commutator, cosocle, hypocenterC13×C17×C25C22
FrattiniC5C2×D1105
FittingC2×C13×C17×C25C2
socleC2×C5×C13×C17D5
LCSG ▷ C13×C17×C25
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 11050

A minimal faithful permutation representation — 2 generators on 57 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);(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)

Conjugacy classes & character table

5528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD22100
maximal normal subgroup ofD22100
maximal quotient ofDic11050, D22100

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22100, 45);