Finite Group Databasebeta

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C13⋊C3×C11⋊#595 #44415751

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

Aliases

direct productC13⋊C3×C11⋊#595
unambiguous semidirect productC11⋊(C13⋊C3×#595)
unambiguous semidirect product(C13×C11⋊#595)⋊C3

Splittings

Fitting, socle, derived, HallC11×C13×C17 ⋊ C3×C4
HallC13×C11⋊#595 ⋊ C3
HallC11×C17×C13⋊C3 ⋊ C4
HallC17×C13⋊C3 ⋊ Dic11
HallC11×C13⋊C3 ⋊ #595
HallC13×C17 ⋊ C3×Dic11
HallC11×C17 ⋊ C4×C13⋊C3
HallC11×C13 ⋊ C3×#595
SylowC17 ⋊ C13⋊C3×Dic11
SylowC13 ⋊ C3×C11⋊#595
SylowC11 ⋊ C13⋊C3×#595

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC11×C13×C17C3×C4
prime radicalC11×D17×C13⋊C3C2
cosocleC11×C13×D17C2×C3
LCSG ▷ C11×C13×C17
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2431

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 43);