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C5×D7×D247 #46829136

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

Aliases

direct productC5×D7×D247
unambiguous semidirect product(C13×D7)⋊(C5×D19)
unambiguous semidirect product(D7×C19)⋊(C5×D13)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5D7×D247
commutator, cosocle, hypocenterC7×C13×C19C22×C5
FrattiniC1G
Fitting, socleC5×C7×C13×C19C22
LCSG ▷ C7×C13×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 8645

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

3125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 27);