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C3×C5×C11⋊#261 #22575121

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

Aliases

direct productC3×C5×C11⋊#261

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C4
derived, HallC11×C13 ⋊ C3×C4×C5
HallC5×C11×C13 ⋊ C3×C4
HallC3×C11×C13 ⋊ C4×C5
HallC3×C5×C13 ⋊ Dic11
HallC3×C5×C11 ⋊ #261
HallC5×C13 ⋊ C3×Dic11
HallC5×C11 ⋊ C3×#261
HallC3×C13 ⋊ C5×Dic11
HallC3×C11 ⋊ C5×#261
SylowC13 ⋊ C3×C5×Dic11
SylowC11 ⋊ C3×C5×#261

Subgroups

subgroupG/H
center, hypercenterC3×C5C11⋊#261
commutator, hypocenterC11×C13C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C13C4
LCSG ▷ C11×C13
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

705 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C11⋊(#261⋊C9), C5×C9×C11⋊#261, C3×C5×C11⋊AGL(1,𝔽13), …
maximal normal subgroup ofC5×C11⋊(#261⋊C9), C5×C9×C11⋊#261, C3×C5×C11⋊AGL(1,𝔽13), …
maximal quotient ofC5×C9×C11⋊#261, C32×C5×C11⋊#261, C3×C5×C3⋊(C11⋊#261)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 93);