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ΓL(1,𝔽8)×C529 #26013169

order11109
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C529 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C529
unambiguous semidirect productC7⋊(C3×C529)
unambiguous semidirect product(C7×C529)⋊C3

Splittings

Fitting, HallC7×C529 ⋊ C3
derived, SylowC7 ⋊ C3×C529

Subgroups

subgroupG/H
center, hypercenterC529ΓL(1,𝔽8)
commutator, hypocenterC7C3×C529
FrattiniC23ΓL(1,𝔽8)×C23
FittingC7×C529C3
socle, cosocleC7×C23C3×C23
prime radicalΓL(1,𝔽8)×C23C23
LCSG ▷ C7
UCSC1 ◁ C529

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2645 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofΓL(1,𝔽8)×D529, AGL(1,𝔽7)×C529, ΓL(1,𝔽8)⋊D529, …
maximal normal subgroup ofΓL(1,𝔽8)×D529, AGL(1,𝔽7)×C529, ΓL(1,𝔽8)⋊D529, …
maximal quotient ofC2×ΓL(1,𝔽8)×C529, C7⋊C9×C529, C3×ΓL(1,𝔽8)×C529

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11109, 2);