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C11×C3⋊#63120 #22575150

order8580
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊#63120
unambiguous semidirect productC3⋊(C11×#63120)

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C4
derived, HallC3×C5×C13 ⋊ C4×C11
HallC5×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ AGL(1,𝔽5)
HallC3×C5×C11 ⋊ Dic13
HallC11×C13 ⋊ ΓL(1,𝔽16)
HallC5×C13 ⋊ C11×Dic3
HallC5×C11 ⋊ Dic39
HallC3×C13 ⋊ C11×AGL(1,𝔽5)
HallC3×C11 ⋊ #63120
HallC3×C5 ⋊ C11×Dic13
SylowC13 ⋊ C11×ΓL(1,𝔽16)
SylowC5 ⋊ C11×Dic39
SylowC3 ⋊ C11×#63120

Subgroups

subgroupG/H
center, hypercenterC11C3⋊#63120
commutator, hypocenterC3×C5×C13C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C13C4
LCSG ▷ C3×C5×C13
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

891 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×C9⋊#63120, C11×C3⋊(#63120⋊C3), C3×C11×C3⋊#63120, …
maximal normal subgroup ofC11×C3⋊(#63120⋊C3), C3×C11×C3⋊#63120
maximal quotient ofC11×C9⋊#63120, C3×C11×C3⋊#63120, C11×C3⋊(C3⋊#63120)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 122);