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C3×C13×Dic11⋊C5 #22575049

order8580
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×Dic11⋊C5
unambiguous semidirect productDic11⋊(C3×C5×C13)
unambiguous semidirect product(C11⋊C5)⋊(C3×C4×C13)
unambiguous semidirect product(C3×Dic11)⋊(C5×C13)
unambiguous semidirect product(C3×C13×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C3×C4×C5×C13
HallC3×C13×C11⋊C5 ⋊ C4
HallC3×C13×Dic11 ⋊ C5
HallC13×C11⋊C5 ⋊ C3×C4
HallC13×Dic11 ⋊ C3×C5
HallC3×C11×C13 ⋊ C4×C5
HallC3×C11⋊C5 ⋊ C4×C13
HallC11×C13 ⋊ C3×C4×C5
HallC3×Dic11 ⋊ C5×C13
HallC11⋊C5 ⋊ C3×C4×C13
HallDic11 ⋊ C3×C5×C13
HallC3×C11 ⋊ C4×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13AGL(1,𝔽11)
commutator, hypocenterC11C3×C4×C5×C13
FrattiniC2C3×C13×AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C13C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

858 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×C13×Dic11⋊C5, C13⋊C9×Dic11⋊C5, C3×C13⋊C3×Dic11⋊C5, …
maximal normal subgroup ofC9×C13×Dic11⋊C5, C13⋊C9×Dic11⋊C5, C3×C13⋊C3×Dic11⋊C5, …
maximal quotient ofC9×C13×Dic11⋊C5, C32×C13×Dic11⋊C5, C3×C13×C3⋊(Dic11⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 21);