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ΓL(1,𝔽8)×C439 #22604279

order9219
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C439 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C439
unambiguous semidirect productC7⋊(C3×C439)

Splittings

Fitting, socle, HallC7×C439 ⋊ C3
derived, SylowC7 ⋊ C3×C439

Subgroups

subgroupG/H
center, hypercenterC439ΓL(1,𝔽8)
commutator, hypocenterC7C3×C439
FrattiniC1G
Fitting, socleC7×C439C3
LCSG ▷ C7
UCSC1 ◁ C439

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2195 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×ΓL(1,𝔽8)×C439, ΓL(1,𝔽8)×D439, AGL(1,𝔽7)×C439, …
maximal normal subgroup ofC2×ΓL(1,𝔽8)×C439, ΓL(1,𝔽8)×D439, AGL(1,𝔽7)×C439, …
maximal quotient ofC2×ΓL(1,𝔽8)×C439, C7⋊C9×C439, C3×ΓL(1,𝔽8)×C439, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9219, 1);