Finite Group Databasebeta

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C13×C13⋊C3×C11⋊C5 #42124197

order27885
automorphism?
homologyAbelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C13⋊C3×C11⋊C5
unambiguous semidirect productC11⋊(C5×C13×C13⋊C3)
unambiguous semidirect productC13⋊(C3×C13×C11⋊C5)
unambiguous semidirect product(C11×C13⋊C3)⋊(C5×C13)
unambiguous semidirect product(C13×C11⋊C5)⋊(C3×C13)
unambiguous semidirect product(C11×C13×C13⋊C3)⋊C5

Splittings

Fitting, socle, HallC11×C132 ⋊ C3×C5
derivedC11×C13 ⋊ C3×C5×C13
HallC132×C11⋊C5 ⋊ C3
HallC11×C13×C13⋊C3 ⋊ C5
SylowC132 ⋊ C3×C11⋊C5
SylowC11 ⋊ C5×C13×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC13C13⋊C3×C11⋊C5
commutator, cosocle, hypocenterC11×C13C3×C5×C13
FrattiniC1G
Fitting, socleC11×C132C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 429

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27885, 6);