Finite Group Databasebeta

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C11×#11725133⋊C3 #44415738

order29172
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#11725133⋊C3
unambiguous semidirect product#11725133⋊(C3×C11)
unambiguous semidirect product(C11×#11725133)⋊C3

Splittings

Fitting, socle, HallC11×C13×C17 ⋊ C3×C4
derived, HallC13×C17 ⋊ C3×C4×C11
HallC11×#11725133 ⋊ C3
HallC11×C17×C13⋊C3 ⋊ C4
Hall#11725133 ⋊ C3×C11
HallC17×C13⋊C3 ⋊ C4×C11
HallC11×C13⋊C3 ⋊ #595
HallC11×C17 ⋊ Dic13⋊C3
HallC11×C13 ⋊ C3×#595
HallC13⋊C3 ⋊ C11×#595
SylowC17 ⋊ C11×Dic13⋊C3
SylowC13 ⋊ C3×C11×#595

Subgroups

subgroupG/H
center, hypercenterC11#11725133⋊C3
commutator, hypocenterC13×C17C3×C4×C11
FrattiniC1G
Fitting, socleC11×C13×C17C3×C4
prime radicalC11×D17×C13⋊C3C2
cosocleC13×D17C2×C3×C11
LCSG ▷ C13×C17
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2431

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 30);