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C2×C5×D1729 #46829192

order34580
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1729
unambiguous semidirect product(C2×C7)⋊(C5×D247)
unambiguous semidirect product(C2×C13)⋊(C5×D133)
unambiguous semidirect product(C2×C19)⋊(C5×D91)

Splittings

Fitting, socleC2×C5×C7×C13×C19 ⋊ C2
derived, HallC7×C13×C19 ⋊ C22×C5
HallC5×C7×C13×C19 ⋊ C22
HallC5×C13×C19 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×D13
HallC5×C7×C13 ⋊ C2×D19
HallC13×C19 ⋊ C2×C5×D7
HallC7×C19 ⋊ C2×C5×D13
HallC5×C19 ⋊ C2×D91
HallC7×C13 ⋊ C2×C5×D19
HallC5×C13 ⋊ C2×D133
HallC5×C7 ⋊ C2×D247
SylowC19 ⋊ C2×C5×D91
SylowC13 ⋊ C2×C5×D133
SylowC7 ⋊ C2×C5×D247

Subgroups

subgroupG/H
center, hypercenterC2×C5D1729
commutator, cosocle, hypocenterC7×C13×C19C22×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C13×C19C2
LCSG ▷ C7×C13×C19
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 17290

A minimal faithful permutation representation — 2 generators on 46 points:

(3,4,5,6,7)(9,10)(11,12)(13,14)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46);(1,2)(8,9,11,13,14,12,10)(15,16,18,20,22,24,26,27,25,23,21,19,17)(28,29,31,33,35,37,39,41,43,45,46,44,42,40,38,36,34,32,30)

Conjugacy classes & character table

8660 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 83);