Finite Group Databasebeta

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C13⋊C9×Dic11⋊C5 #38787804

order25740
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C9×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C13⋊C9)
unambiguous semidirect product(C11⋊C5)⋊(C4×C13⋊C9)
unambiguous semidirect product(C13×Dic11⋊C5)⋊C9
unambiguous semidirect product(Dic11×C13⋊C9)⋊C5

Splittings

derived, HallC11×C13 ⋊ C4×C5×C9
HallC11⋊C5×C13⋊C9 ⋊ C4
HallDic11×C13⋊C9 ⋊ C5
HallC13×Dic11⋊C5 ⋊ C9
HallC11×C13⋊C9 ⋊ C4×C5
HallC13×C11⋊C5 ⋊ C4×C9
HallC13×Dic11 ⋊ C5×C9
HallC11⋊C5 ⋊ C4×C13⋊C9
HallDic11 ⋊ C5×C13⋊C9
SylowC13 ⋊ C9×Dic11⋊C5
SylowC11 ⋊ C4×C5×C13⋊C9

Subgroups

subgroupG/H
center, Frattini, hypercenterC2×C3C13⋊C3×AGL(1,𝔽11)
commutator, hypocenterC11×C13C4×C5×C9
Fitting, socle, cosocleC2×C3×C11×C13C2×C3×C5
prime radicalC2×C3×C13×C11⋊C5C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5148

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 35);