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C2×D4675 #34035161

order18700
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9350
direct productC2×D4675
unambiguous semidirect product(C2×C11)⋊D425
unambiguous semidirect product(C2×C17)⋊D275
unambiguous semidirect product(C2×C25)⋊D187

Splittings

FittingC2×C11×C17×C25 ⋊ C2
derived, HallC11×C17×C25 ⋊ C22
HallC17×C25 ⋊ C2×D11
HallC11×C25 ⋊ C2×D17
HallC11×C17 ⋊ C2×D25
SylowC25 ⋊ C2×D187
SylowC17 ⋊ C2×D275
SylowC11 ⋊ C2×D425

Subgroups

subgroupG/H
center, hypercenterC2D4675
commutator, cosocle, hypocenterC11×C17×C25C22
FrattiniC5C2×D935
FittingC2×C11×C17×C25C2
socleC2×C5×C11×C17D5
LCSG ▷ C11×C17×C25
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 9350

A minimal faithful permutation representation — 2 generators on 55 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);(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)(40,55)(41,54)(42,53)(43,52)(44,51)(45,50)(46,49)(47,48)

Conjugacy classes & character table

4678 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD18700, C2×D14025
maximal normal subgroup ofD18700
maximal quotient ofDic9350, D18700, C2×D14025

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 46);