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(#16812968⋊C2)⋊C5 #47977602

order35340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(#16812968⋊C2)⋊C5
unambiguous semidirect product(#16812968⋊C5)⋊C2
unambiguous semidirect product(#16812972⋊C5)⋊C2
unambiguous semidirect product(#16812976⋊C5)⋊C2

Splittings

Fitting, socle, derived, HallC19×C31 ⋊ C22×C3×C5
HallD19×D31⋊C5 ⋊ C3
Hall#13183714⋊C5 ⋊ C22
Hall#16812968⋊C2 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C22×C3
HallD19×D31 ⋊ C3×C5
Hall#13183714 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C2×D19⋊C3
SylowC31 ⋊ C2×C5×D19⋊C3
SylowC19 ⋊ C2×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC19×C31C22×C3×C5
LCSG ▷ C19×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 589

A minimal faithful permutation representation — 2 generators on 50 points:

(2,6,7,3,4,8)(5,14,11,9,10,16)(12,17,19,18,15,13)(20,21,41,25,30,24,34,26,43,47,36,29,27,38,50)(22,44,23,33,37,48,28,32,39,40,31,46,42,35,45);(1,2,5,11,17,14,18,4,8,13,19,7,6,12,10,15,16,9,3)(21,22)(23,26)(24,27)(25,33)(28,30)(29,36)(31,38)(32,44)(34,46)(35,39)(37,43)(40,48)(41,50)(42,45)(47,49)

Polycyclic presentation:

2^2,3,5,19,31|f^a=f^30,e^b=e^18,e^c=e^7,f^c=f^5,f^d=f^16

Conjugacy classes & character table

101 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 74);