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C5×C11⋊(D13⋊C3) #16864264

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

Aliases

direct productC5×C11⋊(D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C5×D11)
unambiguous semidirect product(C5×D143)⋊C3

Splittings

Fitting, socle, HallC5×C11×C13 ⋊ C2×C3
derived, HallC11×C13 ⋊ C2×C3×C5
HallC5×C11×C13⋊C3 ⋊ C2
HallC5×D143 ⋊ C3
HallC11×C13⋊C3 ⋊ C2×C5
HallD143 ⋊ C3×C5
HallC5×C13⋊C3 ⋊ D11
HallC5×C13 ⋊ C3×D11
HallC5×C11 ⋊ D13⋊C3
HallC13⋊C3 ⋊ C5×D11
SylowC13 ⋊ C3×C5×D11
SylowC11 ⋊ C5×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C11⋊(D13⋊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

Conjugacy classes & character table

215 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×C11⋊(D13⋊C3), C5×C3⋊(C11⋊(D13⋊C3)), C25×C11⋊(D13⋊C3), …
maximal normal subgroup ofC3×C5×C11⋊(D13⋊C3), C25×C11⋊(D13⋊C3), (C13⋊C3)⋊(D11⋊C25), …
maximal quotient ofC5×C11⋊(D13⋊C9), C3×C5×C11⋊(D13⋊C3), C5×C3⋊(C11⋊(D13⋊C3)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 29);