Finite Group Databasebeta

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C13×C49×C11⋊C5 #46856217

order35035
automorphism?
homologyAbelianization (H1) = C5×C13×C49 · Schur multiplier (H2) = C1

Aliases

direct productC13×C49×C11⋊C5
unambiguous semidirect productC11⋊(C5×C13×C49)
unambiguous semidirect product(C11×C13)⋊(C5×C49)
unambiguous semidirect product(C11×C49)⋊(C5×C13)
unambiguous semidirect product(C11×C13×C49)⋊C5

Splittings

Fitting, HallC11×C13×C49 ⋊ C5
derived, SylowC11 ⋊ C5×C13×C49
HallC11×C49 ⋊ C5×C13
HallC11×C13 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC13×C49C11⋊C5
commutator, hypocenterC11C5×C13×C49
FrattiniC7C7×C13×C11⋊C5
FittingC11×C13×C49C5
socleC7×C11×C13C5×C7
prime radicalC7×C13×C11⋊C5C7
cosocleC7×C11C5×C7×C13
LCSG ▷ C11
UCSC1 ◁ C13×C49

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7007

Conjugacy classes & character table

4459 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35035, 2);