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C52×ΓL(1,𝔽8)×D11 #26040499

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×ΓL(1,𝔽8)×D11

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC52ΓL(1,𝔽8)×D11
commutator, cosocle, hypocenterC7×C11C2×C3×C52
FrattiniC1G
Fitting, socleC52×C7×C11C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C52

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

875 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC52×D11×AGL(1,𝔽7), C5×D11×C5⋊AGL(1,𝔽7), C5×D5×ΓL(1,𝔽8)×D11, …
maximal normal subgroup ofC52×D11×AGL(1,𝔽7), C5×D11×C5⋊AGL(1,𝔽7), C5×D5×ΓL(1,𝔽8)×D11, …
maximal quotient ofC52×ΓL(1,𝔽8)×Dic11, C2×C52×ΓL(1,𝔽8)×D11, C52×D11×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 63);