Finite Group Databasebeta

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C3×C13×C11⋊#595 #44415767

order29172
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×C11⋊#595
unambiguous semidirect productC11⋊(C3×C13×#595)

Splittings

Fitting, socle, HallC3×C11×C13×C17 ⋊ C4
derived, HallC11×C17 ⋊ C3×C4×C13
HallC11×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ Dic11
HallC3×C11×C17 ⋊ C4×C13
HallC3×C11×C13 ⋊ #595
HallC13×C17 ⋊ C3×Dic11
HallC11×C13 ⋊ C3×#595
HallC3×C17 ⋊ C13×Dic11
HallC3×C11 ⋊ C13×#595
SylowC17 ⋊ C3×C13×Dic11
SylowC11 ⋊ C3×C13×#595

Subgroups

subgroupG/H
center, hypercenterC3×C13C11⋊#595
commutator, hypocenterC11×C17C3×C4×C13
FrattiniC1G
Fitting, socleC3×C11×C13×C17C4
prime radicalC3×C11×C13×D17C2
cosocleC11×D17C2×C3×C13
LCSG ▷ C11×C17
UCSC1 ◁ C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7293

Conjugacy classes & character table

2262 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 59);