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D3×C5⋊(D71⋊C7) #44447180

order29820
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productD3×C5⋊(D71⋊C7)
unambiguous semidirect product(C5×D3)⋊(D71⋊C7)
unambiguous semidirect product(D3×C71⋊C7)⋊D5
unambiguous semidirect product(D3×D355)⋊C7

Splittings

Fitting, socle, derived, HallC3×C5×C71 ⋊ C22×C7
HallC3×C5×C71⋊C7 ⋊ C22
HallD3×D355 ⋊ C7
HallC5×C71⋊C7 ⋊ C2×D3
HallC3×C71⋊C7 ⋊ C2×D5
HallC71⋊C7 ⋊ D3×D5
HallC5×C71 ⋊ C2×D3×C7
HallC3×C71 ⋊ C2×C7×D5
SylowC71 ⋊ D3×C7×D5
HallC3×C5 ⋊ C2×D71⋊C7
SylowC5 ⋊ D3×D71⋊C7
SylowC3 ⋊ C2×C5⋊(D71⋊C7)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C71C22×C7
LCSG ▷ C3×C5×C71
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 79
transitive degreeμt(G) = 1065

A minimal faithful permutation representation — 2 generators on 79 points:

(1,2,3)(5,6)(7,8)(10,14,15,32,28,62,63,11,12,20,22,45,43,71)(13,27,19,47,48,16,39,17,18,29,30,70,24,25)(21,54,51,60,56,44,57,34,35,73,40,36,65,66)(23,49,58,76,68,69,31,37,38,72,55,46,64,50)(26,61,33,74,75,78,59,41,42,52,53,67,79,77);(2,3)(4,5,7,8,6)(9,10,13,19,31,51,38,47,35,55,77,25,40,53,72,61,78,75,65,18,28,46,69,62,41,24,14,21,36,57,63,70,22,37,20,33,52,15,23,32,48,71,66,56,34,12,16,26,43,64,68,45,27,44,67,79,42,58,74,60,39,59,76,54,30,49,73,50,29,17,11)

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 68);