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C2×#16812976⋊C5 #47977607

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

Aliases

direct productC2×#16812976⋊C5
unambiguous semidirect product(C2×#16812976)⋊C5

Splittings

Fitting, socleC2×C19×C31 ⋊ C2×C3×C5
derived, HallC19×C31 ⋊ C22×C3×C5
HallC2×C19⋊(D31⋊C5) ⋊ C3
Hall#13183714⋊C5 ⋊ C22
HallC2×#16812976 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C22×C3
HallC2×D589 ⋊ 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, hypercenterC2#16812976⋊C5
commutator, cosocle, hypocenterC19×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C19×C31C2×C3×C5
LCSG ▷ C19×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 1178

A minimal faithful permutation representation — 2 generators on 52 points:

(4,8,9,5,6,10)(7,16,13,11,12,18)(14,19,21,20,17,15)(23,38,46,39,36,32,26,50,44,35,25,37,33,49,43,24,31,34,45,48,30,29,42,47,27,28,41,40,51,52);(1,2)(3,4,7,13,19,16,20,6,10,15,21,9,8,14,12,17,18,11,5)(22,23,27,37,45,25,32,44,33,42,36,49,52,38,46,29,26,34,31,43,51,48,50,40,47,30,28,39,41,35,24)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 79);