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C2×D4505 #31825145

order18020
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9010
direct productC2×D4505
unambiguous semidirect product(C2×C5)⋊D901
unambiguous semidirect product(C2×C17)⋊D265
unambiguous semidirect product(C2×C53)⋊D85

Splittings

Fitting, socleC2×C5×C17×C53 ⋊ C2
derived, HallC5×C17×C53 ⋊ C22
HallC17×C53 ⋊ C2×D5
HallC5×C53 ⋊ C2×D17
HallC5×C17 ⋊ C2×D53
SylowC53 ⋊ C2×D85
SylowC17 ⋊ C2×D265
SylowC5 ⋊ C2×D901

Subgroups

subgroupG/H
center, hypercenterC2D4505
commutator, cosocle, hypocenterC5×C17×C53C22
FrattiniC1G
Fitting, socleC2×C5×C17×C53C2
LCSG ▷ C5×C17×C53
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 77
transitive degreeμt(G) = 9010

A minimal faithful permutation representation — 2 generators on 77 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);(4,7)(5,6)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Conjugacy classes & character table

4508 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD18020, C2×D13515
maximal normal subgroup ofD18020
maximal quotient ofDic9010, D18020, C2×D13515

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18020, 45);