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C17×C11⋊(D13⋊C3) #28410210

order14586
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C11⋊(D13⋊C3)
unambiguous semidirect productC11⋊(C17×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C17×D11)
unambiguous semidirect productD143⋊(C3×C17)
unambiguous semidirect product(C17×D143)⋊C3

Splittings

Fitting, socle, HallC11×C13×C17 ⋊ C2×C3
derived, HallC11×C13 ⋊ C2×C3×C17
HallC11×C17×C13⋊C3 ⋊ C2
HallC17×D143 ⋊ C3
HallC17×C13⋊C3 ⋊ D11
HallC11×C13⋊C3 ⋊ C2×C17
HallD143 ⋊ C3×C17
HallC13×C17 ⋊ C3×D11
HallC11×C17 ⋊ D13⋊C3
HallC13⋊C3 ⋊ C17×D11
SylowC13 ⋊ C3×C17×D11
SylowC11 ⋊ C17×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC17C11⋊(D13⋊C3)
commutator, cosocle, hypocenterC11×C13C2×C3×C17
FrattiniC1G
Fitting, socleC11×C13×C17C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2431

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD17×C11⋊(D13⋊C3), C17×D11×D13⋊C3, D187⋊(D13⋊C3), …
maximal normal subgroup ofD17×C11⋊(D13⋊C3), C17×D11×D13⋊C3, D187⋊(D13⋊C3), …
maximal quotient ofC17×C11⋊(Dic13⋊C3), C2×C17×C11⋊(D13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14586, 23);