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C52×ΓL(1,𝔽8)2 #26010609

order11025
automorphism?
homologyAbelianization (H1) = C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC52×ΓL(1,𝔽8)2
unambiguous semidirect product(C7×ΓL(1,𝔽8))⋊(C3×C52)
unambiguous semidirect product#3861⋊(C3×C52)
unambiguous semidirect product#3862⋊(C3×C52)
unambiguous semidirect product(C5×C7×ΓL(1,𝔽8))⋊(C3×C5)
unambiguous semidirect product(C5×#3861)⋊(C3×C5)
unambiguous semidirect product(C5×#3862)⋊(C3×C5)

Splittings

Fitting, socle, HallC52×C72 ⋊ C32
derived, SylowC72 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC52ΓL(1,𝔽8)2
commutator, cosocle, hypocenterC72C32×C52
FrattiniC1G
Fitting, socleC52×C72C32
LCSG ▷ C72
UCSC1 ◁ C52

224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

625 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC52×#64418⋊C3, C52×ΓL(1,𝔽8)×AGL(1,𝔽7), C52×ΓL(1,𝔽8)⋊AGL(1,𝔽7), …
maximal normal subgroup ofC52×#64418⋊C3, C52×ΓL(1,𝔽8)×AGL(1,𝔽7), C52×ΓL(1,𝔽8)⋊AGL(1,𝔽7), …
maximal quotient ofC2×C52×ΓL(1,𝔽8)2

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11025, 32);