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C13×C3⋊(Dic11⋊C5) #22575053

order8580
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊(Dic11⋊C5)
unambiguous semidirect productC3⋊(C13×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(Dic3×C13)
unambiguous semidirect productDic33⋊(C5×C13)
unambiguous semidirect product(C13×Dic33)⋊C5

Splittings

derived, HallC3×C11 ⋊ C4×C5×C13
HallC3×C13×C11⋊C5 ⋊ C4
HallC13×Dic33 ⋊ C5
HallC13×C11⋊C5 ⋊ Dic3
HallC3×C11×C13 ⋊ C4×C5
HallC3×C11⋊C5 ⋊ C4×C13
HallC11×C13 ⋊ C5×Dic3
HallDic33 ⋊ C5×C13
HallC11⋊C5 ⋊ Dic3×C13
HallC3×C13 ⋊ Dic11⋊C5
SylowC11 ⋊ C5×Dic3×C13
SylowC3 ⋊ C13×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C4×C5×C13
FrattiniC2C13×C3⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C13C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

468 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×C9⋊(Dic11⋊C5), C13⋊C3×C3⋊(Dic11⋊C5), C3×C13×C3⋊(Dic11⋊C5), …
maximal normal subgroup ofC13⋊C3×C3⋊(Dic11⋊C5), C3×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, 25);