Finite Group Databasebeta

← Prev (#21441219) Next (#21441221) →

C7×ΓL(1,𝔽8)×C53 #21441220

order7791
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C7×C53 · Schur multiplier (H2) = C1

Aliases

direct productC7×ΓL(1,𝔽8)×C53
unambiguous semidirect productC7⋊(C3×C7×C53)
unambiguous semidirect product(C7×C53)⋊(C3×C7)

Splittings

Fitting, socle, HallC72×C53 ⋊ C3
derivedC7 ⋊ C3×C7×C53
SylowC72 ⋊ C3×C53

Subgroups

subgroupG/H
center, hypercenterC7×C53ΓL(1,𝔽8)
commutator, hypocenterC7C3×C7×C53
FrattiniC1G
Fitting, socleC72×C53C3
LCSG ▷ C7
UCSC1 ◁ C7×C53

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1855 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×AGL(1,𝔽7)×C53, C7×ΓL(1,𝔽8)⋊D53, C7×ΓL(1,𝔽8)×D53, …
maximal normal subgroup ofC7×AGL(1,𝔽7)×C53, C7×ΓL(1,𝔽8)⋊D53, C7×ΓL(1,𝔽8)×D53, …
maximal quotient ofC2×C7×ΓL(1,𝔽8)×C53, C7×C53×C7⋊C9, C3×C7×ΓL(1,𝔽8)×C53, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7791, 5);