Finite Group Databasebeta

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C13⋊C3×Dic11⋊C5 #22575063

order8580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C13⋊C3)
unambiguous semidirect product(C11⋊C5)⋊(C4×C13⋊C3)
unambiguous semidirect product(C13⋊C3×Dic11)⋊C5
unambiguous semidirect product(C13×Dic11⋊C5)⋊C3

Splittings

derived, HallC11×C13 ⋊ C3×C4×C5
HallC13×Dic11⋊C5 ⋊ C3
HallC13⋊C3×C11⋊C5 ⋊ C4
HallC13⋊C3×Dic11 ⋊ C5
HallC13×C11⋊C5 ⋊ C3×C4
HallC13×Dic11 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C4×C5
HallC11⋊C5 ⋊ C4×C13⋊C3
HallDic11 ⋊ C5×C13⋊C3
SylowC13 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C4×C5×C13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C13⋊C3×AGL(1,𝔽11)
commutator, hypocenterC11×C13C3×C4×C5
Fitting, socleC2×C11×C13C2×C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C13⋊C3×Dic11⋊C5, C13⋊C3×C3⋊(Dic11⋊C5)
maximal normal subgroup ofC3×C13⋊C3×Dic11⋊C5
maximal quotient ofC13⋊C9×Dic11⋊C5, C3×C13⋊C3×Dic11⋊C5, C13⋊C3×C3⋊(Dic11⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 35);