Finite Group Databasebeta

← Prev (#28384646) Next (#28384648) →

C2×D13×C11⋊C25 #28384647

order14300
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×D13×C11⋊C25
unambiguous semidirect productC13⋊(C22×C11⋊C25)
unambiguous semidirect product(C2×C13)⋊(C2×C11⋊C25)
unambiguous semidirect product(C2×C11×D13)⋊C25

Splittings

derived, HallC11×C13 ⋊ C22×C25
HallC13×C11⋊C25 ⋊ C22
HallC2×C11×D13 ⋊ C25
SylowC13 ⋊ C22×C11⋊C25
SylowC11 ⋊ C2×C25×D13

Subgroups

subgroupG/H
center, hypercenterC2×C5D13×C11⋊C5
commutator, hypocenterC11×C13C22×C25
FrattiniC5C2×D13×C11⋊C5
Fitting, socleC2×C5×C11×C13C2×C5
prime radicalC2×C5×C11×D13C5
cosocleC5×C11×C13C22×C5
LCSG ▷ C11×C13
UCSC1 ◁ C2×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7150

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14300, 19);