Finite Group Databasebeta

← Prev (#27211527) Next (#27211529) →

C3×C11×D29⋊C7 #27211528

order13398
isoclinismisoclinic class of D29⋊C7
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D29⋊C7
unambiguous semidirect productD29⋊(C3×C7×C11)
unambiguous semidirect product(C3×D29)⋊(C7×C11)
unambiguous semidirect product(C29⋊C7)⋊(C2×C3×C11)
unambiguous semidirect product(C11×D29)⋊(C3×C7)
unambiguous semidirect product(C3×C11×D29)⋊C7

Splittings

Fitting, socle, HallC3×C11×C29 ⋊ C2×C7
derived, SylowC29 ⋊ C2×C3×C7×C11
HallC3×C11×C29⋊C7 ⋊ C2
HallC11×C29⋊C7 ⋊ C2×C3
HallC3×C11×D29 ⋊ C7
HallC11×D29 ⋊ C3×C7
HallC3×C29⋊C7 ⋊ C2×C11
HallC11×C29 ⋊ C2×C3×C7
HallC29⋊C7 ⋊ C2×C3×C11
HallC3×D29 ⋊ C7×C11
HallC3×C29 ⋊ C2×C7×C11
HallD29 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11D29⋊C7
commutator, cosocle, hypocenterC29C2×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C11×C29C2×C7
LCSG ▷ C29
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 957

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

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

Conjugacy classes & character table

528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×AGL(1,𝔽29), C3×C11⋊AGL(1,𝔽29), C3×D11×D29⋊C7, …
maximal normal subgroup ofC3×C11×AGL(1,𝔽29), C3×C11⋊AGL(1,𝔽29), C3×D11×D29⋊C7, …
maximal quotient ofC3×C11×Dic29⋊C7, C2×C3×C11×D29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 19);