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C3×#261×C11⋊C5 #22575074

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

Aliases

direct productC3×#261×C11⋊C5
unambiguous semidirect product(C3×C11×#261)⋊C5

Splittings

Fitting, socle, HallC3×C11×C13 ⋊ C4×C5
derived, HallC11×C13 ⋊ C3×C4×C5
HallC3×C13×C11⋊C5 ⋊ C4
HallC3×C11×#261 ⋊ C5
HallC13×C11⋊C5 ⋊ C3×C4
HallC11×#261 ⋊ C3×C5
HallC3×C13 ⋊ C4×C11⋊C5
HallC3×C11 ⋊ C5×#261
SylowC13 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C3×C5×#261

Subgroups

subgroupG/H
center, hypercenterC3#261×C11⋊C5
commutator, hypocenterC11×C13C3×C4×C5
FrattiniC1G
Fitting, socleC3×C11×C13C4×C5
LCSG ▷ C11×C13
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×#261⋊C9, C9×#261×C11⋊C5, C3×C11⋊C5×AGL(1,𝔽13), …
maximal normal subgroup ofC11⋊C5×#261⋊C9, C9×#261×C11⋊C5, C3×C11⋊C5×AGL(1,𝔽13), …
maximal quotient ofC9×#261×C11⋊C5, C32×#261×C11⋊C5, C3×C11⋊C5×C3⋊#261

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 46);