Finite Group Databasebeta

← Prev (#44473270) Next (#44473272) →

C3⋊(C7⋊(C13⋊AGL(1,𝔽11))) #44473271

order30030
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C7⋊(C13⋊AGL(1,𝔽11)))
unambiguous semidirect productC7⋊(C3⋊(C13⋊AGL(1,𝔽11)))
unambiguous semidirect productC13⋊(C3⋊(C7⋊AGL(1,𝔽11)))
unambiguous semidirect product(C11⋊C5)⋊D273
unambiguous semidirect productD3003⋊C5

Splittings

Fitting, socle, derived, HallC3×C7×C11×C13 ⋊ C2×C5
HallC3×C7×C13×C11⋊C5 ⋊ C2
HallD3003 ⋊ C5
HallC7×C13×C11⋊C5 ⋊ D3
HallC3×C13×C11⋊C5 ⋊ D7
HallC3×C7×C11⋊C5 ⋊ D13
HallC7×C11×C13 ⋊ C5×D3
HallC13×C11⋊C5 ⋊ D21
HallC3×C11×C13 ⋊ C5×D7
HallC7×C11⋊C5 ⋊ D39
HallC3×C7×C13 ⋊ AGL(1,𝔽11)
HallC3×C7×C11 ⋊ C5×D13
HallC3×C11⋊C5 ⋊ D91
HallC11×C13 ⋊ C5×D21
HallC7×C13 ⋊ C3⋊AGL(1,𝔽11)
HallC7×C11 ⋊ C5×D39
HallC11⋊C5 ⋊ D273
HallC3×C13 ⋊ C7⋊AGL(1,𝔽11)
HallC3×C11 ⋊ C5×D91
HallC3×C7 ⋊ C13⋊AGL(1,𝔽11)
SylowC13 ⋊ C3⋊(C7⋊AGL(1,𝔽11))
SylowC11 ⋊ C5×D273
SylowC7 ⋊ C3⋊(C13⋊AGL(1,𝔽11))
SylowC3 ⋊ C7⋊(C13⋊AGL(1,𝔽11))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C13C2×C5
LCSG ▷ C3×C7×C11×C13
UCSC1

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 3003

A minimal faithful permutation representation — 2 generators on 34 points:

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

Polycyclic presentation:

2,3,5,7,11,13|b^a=b^2,d^a=d^6,e^a=e^10,f^a=f^12,e^c=e^4

Conjugacy classes & character table

963 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 56);