Finite Group Databasebeta

← Prev (#16864262) Next (#16864264) →

C5×D11×C13⋊C3 #16864263

order4290
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D11×C13⋊C3
unambiguous semidirect product(C5×C13×D11)⋊C3

Splittings

Fitting, socle, HallC5×C11×C13 ⋊ C2×C3
derived, HallC11×C13 ⋊ C2×C3×C5
HallC5×C11×C13⋊C3 ⋊ C2
HallC5×C13×D11 ⋊ C3
HallC11×C13⋊C3 ⋊ C2×C5
HallC13×D11 ⋊ C3×C5
HallC5×C13 ⋊ C3×D11
HallC5×C11 ⋊ C2×C13⋊C3
SylowC13 ⋊ C3×C5×D11
SylowC11 ⋊ C2×C5×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D11×C13⋊C3
commutator, cosocle, hypocenterC11×C13C2×C3×C5
FrattiniC1G
Fitting, socleC5×C11×C13C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 715

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D11×C13⋊C3, C5×C13⋊C3×D33, D11×C25×C13⋊C3, …
maximal normal subgroup ofC3×C5×D11×C13⋊C3, D11×C25×C13⋊C3, C13⋊C3×D11⋊C25, …
maximal quotient ofC5×D11×C13⋊C9, C3×C5×D11×C13⋊C3, C5×C13⋊C3×D33, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 28);