Finite Group Databasebeta

← Prev (#27189187) Next (#27189189) →

C2×C3⋊(C7⋊(D31⋊C5)) #27189188

order13020
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(C7⋊(D31⋊C5))
unambiguous semidirect product(C2×C3)⋊(C7⋊(D31⋊C5))
unambiguous semidirect product(C2×C7)⋊(C3⋊(D31⋊C5))
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊D21
unambiguous semidirect product(C2×D651)⋊C5

Splittings

Fitting, socleC2×C3×C7×C31 ⋊ C2×C5
derived, HallC3×C7×C31 ⋊ C22×C5
HallC3×C7×ΓL(1,𝔽32) ⋊ C22
HallC2×D651 ⋊ C5
HallC7×ΓL(1,𝔽32) ⋊ C2×D3
HallC3×ΓL(1,𝔽32) ⋊ C2×D7
HallC7×C31 ⋊ C2×C5×D3
HallΓL(1,𝔽32) ⋊ C2×D21
HallC3×C31 ⋊ C2×C5×D7
SylowC31 ⋊ C2×C5×D21
HallC3×C7 ⋊ C2×D31⋊C5
SylowC7 ⋊ C2×C3⋊(D31⋊C5)
SylowC3 ⋊ C2×C7⋊(D31⋊C5)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C7⋊(D31⋊C5))
commutator, cosocle, hypocenterC3×C7×C31C22×C5
FrattiniC1G
Fitting, socleC2×C3×C7×C31C2×C5
LCSG ▷ C3×C7×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 1302

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 155);