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C11⋊C5×#63270 #28418532

order15015
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×#63270
unambiguous semidirect productC11⋊(C5×#63270)
unambiguous semidirect product(C11×#63270)⋊C5

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C3×C5
HallC7×C13×C11⋊C5 ⋊ C3
HallC11×#63270 ⋊ C5
HallC13×C11⋊C5 ⋊ ΓL(1,𝔽8)
HallC7×C11⋊C5 ⋊ C13⋊C3
HallC11×C13 ⋊ C5×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×C11⋊C5
HallC7×C11 ⋊ C5×C13⋊C3
SylowC13 ⋊ ΓL(1,𝔽8)×C11⋊C5
SylowC11 ⋊ C5×#63270
SylowC7 ⋊ C13⋊C3×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C13C3×C5
LCSG ▷ C7×C11×C13
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1001

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11⋊C5×#63270, C11⋊C5×#10587716, AGL(1,𝔽11)×#63270, …
maximal normal subgroup ofC2×C11⋊C5×#63270, C11⋊C5×#10587716, AGL(1,𝔽11)×#63270, …
maximal quotient ofC2×C11⋊C5×#63270

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15015, 9);