Finite Group Databasebeta

← Prev (#28410188) Next (#28410190) →

C2×C11×C17×C13⋊C3 #28410189

order14586
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×C17×C13⋊C3
unambiguous semidirect product(C2×C13)⋊(C3×C11×C17)
unambiguous semidirect product(C2×C11×C13)⋊(C3×C17)
unambiguous semidirect product(C2×C13×C17)⋊(C3×C11)
unambiguous semidirect product(C2×C11×C13×C17)⋊C3

Splittings

Fitting, socle, HallC2×C11×C13×C17 ⋊ C3
derived, SylowC13 ⋊ C2×C3×C11×C17
HallC11×C13×C17 ⋊ C2×C3
HallC2×C13×C17 ⋊ C3×C11
HallC2×C11×C13 ⋊ C3×C17
HallC13×C17 ⋊ C2×C3×C11
HallC11×C13 ⋊ C2×C3×C17
HallC2×C13 ⋊ C3×C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17C13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C11×C17
FrattiniC1G
Fitting, socleC2×C11×C13×C17C3
LCSG ▷ C13
UCSC1 ◁ C2×C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4862

Conjugacy classes & character table

2618 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C11×C17×C13⋊C3, C11×C13⋊C3×Dic17, C11×C17×Dic13⋊C3, …
maximal normal subgroup ofC4×C11×C17×C13⋊C3, C11×C13⋊C3×Dic17, C11×C17×Dic13⋊C3, …
maximal quotient ofC4×C11×C17×C13⋊C3, C22×C11×C17×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14586, 2);