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D11×C7⋊(C52⋊C3) #26040523

order11550
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

direct productD11×C7⋊(C52⋊C3)
unambiguous semidirect productC11⋊(C2×C7⋊(C52⋊C3))
unambiguous semidirect product(C7×D11)⋊(C52⋊C3)
unambiguous semidirect product(C52×D11)⋊ΓL(1,𝔽8)

Splittings

Fitting, socle, derived, HallC52×C7×C11 ⋊ C2×C3
HallC11×C7⋊(C52⋊C3) ⋊ C2
HallC52×C7×D11 ⋊ C3
HallC52×D11 ⋊ ΓL(1,𝔽8)
HallC52×C11 ⋊ C2×ΓL(1,𝔽8)
HallC52×C7 ⋊ C3×D11
HallC7×D11 ⋊ C52⋊C3
HallC7×C11 ⋊ C2×C52⋊C3
SylowC52 ⋊ ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×C7⋊(C52⋊C3)
SylowC7 ⋊ D11×C52⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C11C2×C3
LCSG ▷ C52×C7×C11
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

427 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×D7⋊(C52⋊C3), D11×#11760386, D11×(C5⋊D5)⋊ΓL(1,𝔽8), …
maximal normal subgroup ofD11×D7⋊(C52⋊C3), D11×#11760386, D11×(C5⋊D5)⋊ΓL(1,𝔽8), …
maximal quotient ofDic11×C7⋊(C52⋊C3), C2×D11×C7⋊(C52⋊C3), D11×C7⋊(C52⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 87);