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C2×D5225 #35229848

order20900
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD10450
direct productC2×D5225
unambiguous semidirect product(C2×C11)⋊D475
unambiguous semidirect product(C2×C19)⋊D275
unambiguous semidirect product(C2×C25)⋊D209

Splittings

FittingC2×C11×C19×C25 ⋊ C2
derived, HallC11×C19×C25 ⋊ C22
HallC19×C25 ⋊ C2×D11
HallC11×C25 ⋊ C2×D19
HallC11×C19 ⋊ C2×D25
SylowC25 ⋊ C2×D209
SylowC19 ⋊ C2×D275
SylowC11 ⋊ C2×D475

Subgroups

subgroupG/H
center, hypercenterC2D5225
commutator, cosocle, hypocenterC11×C19×C25C22
FrattiniC5C2×D1045
FittingC2×C11×C19×C25C2
socleC2×C5×C11×C19D5
LCSG ▷ C11×C19×C25
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 10450

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)(29,38)(30,37)(31,36)(32,35)(33,34)(40,57)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)

Conjugacy classes & character table

5228 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD20900, C2×D15675
maximal normal subgroup ofD20900
maximal quotient ofDic10450, D20900, C2×D15675

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 30);