Finite Group Databasebeta

← Prev (#47977602) Next (#47977604) →

(#16812967⋊C2)⋊C5 #47977603

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

Aliases

unambiguous semidirect product(#16812967⋊C2)⋊C5
unambiguous semidirect product(#16812967⋊C5)⋊C2
unambiguous semidirect product(#16812971⋊C5)⋊C2
unambiguous semidirect product(#16812975⋊C5)⋊C2

Splittings

Fitting, socle, derived, HallC19×C31 ⋊ C22×C3×C5
HallD19×D31⋊C5 ⋊ C3
Hall#13183715⋊C5 ⋊ C22
Hall#16812967⋊C2 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C22×C3
HallD19×D31 ⋊ C3×C5
Hall#13183715 ⋊ 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)(20,21,33,36,49,22,42,48,35,37,23,34,26,39,50)(24,27,38,43,28,32,46,41,40,45,44,29,47,25,30);(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)(29,35)(31,37)(32,39)(34,46)(36,45)(38,40)(41,42)(43,44)(47,50)(48,49)

Polycyclic presentation:

2^2,3,5,19,31|f^a=f^30,e^b=e^18,e^c=e^7,f^c=f^25,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, 75);