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C2×D4921 #34088977

order19684
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9842
direct productC2×D4921
unambiguous semidirect product(C2×C7)⋊D703
unambiguous semidirect product(C2×C19)⋊D259
unambiguous semidirect product(C2×C37)⋊D133

Splittings

Fitting, socleC2×C7×C19×C37 ⋊ C2
derived, HallC7×C19×C37 ⋊ C22
HallC19×C37 ⋊ C2×D7
HallC7×C37 ⋊ C2×D19
HallC7×C19 ⋊ C2×D37
SylowC37 ⋊ C2×D133
SylowC19 ⋊ C2×D259
SylowC7 ⋊ C2×D703

Subgroups

subgroupG/H
center, hypercenterC2D4921
commutator, cosocle, hypocenterC7×C19×C37C22
FrattiniC1G
Fitting, socleC2×C7×C19×C37C2
LCSG ▷ C7×C19×C37
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 65
transitive degreeμt(G) = 9842

A minimal faithful permutation representation — 2 generators on 65 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);(4,9)(5,8)(6,7)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60)(36,59)(37,58)(38,57)(39,56)(40,55)(41,54)(42,53)(43,52)(44,51)(45,50)(46,49)(47,48)

Conjugacy classes & character table

4924 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD19684, C2×D14763
maximal normal subgroup ofD19684
maximal quotient ofDic9842, D19684, C2×D14763

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19684, 21);