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C3×C11⋊#63122 #22575128

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

Aliases

direct productC3×C11⋊#63122
unambiguous semidirect productC11⋊(C3×#63122)

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C4
derived, HallC5×C11×C13 ⋊ C3×C4
HallC3×C11×C13 ⋊ AGL(1,𝔽5)
HallC3×C5×C13 ⋊ Dic11
HallC3×C5×C11 ⋊ #261
HallC11×C13 ⋊ C3×AGL(1,𝔽5)
HallC5×C13 ⋊ C3×Dic11
HallC5×C11 ⋊ C3×#261
HallC3×C13 ⋊ C11⋊AGL(1,𝔽5)
HallC3×C11 ⋊ #63122
HallC3×C5 ⋊ C11⋊#261
SylowC13 ⋊ C3×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ C3×#63122
SylowC5 ⋊ C3×C11⋊#261

Subgroups

subgroupG/H
center, hypercenterC3C11⋊#63122
commutator, hypocenterC5×C11×C13C3×C4
FrattiniC1G
Fitting, socleC3×C5×C11×C13C4
LCSG ▷ C5×C11×C13
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊(#63122⋊C9), C9×C11⋊#63122, C3×C11⋊(#63122⋊C3), …
maximal normal subgroup ofC11⋊(#63122⋊C9), C9×C11⋊#63122, C3×C11⋊(#63122⋊C3), …
maximal quotient ofC9×C11⋊#63122, C32×C11⋊#63122, C3×C3⋊(C11⋊#63122)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 100);