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ΓL(1,𝔽8)×C313 #20267158

order6573
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C313 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C313
unambiguous semidirect productC7⋊(C3×C313)

Splittings

Fitting, socle, HallC7×C313 ⋊ C3
derived, SylowC7 ⋊ C3×C313

Subgroups

subgroupG/H
center, hypercenterC313ΓL(1,𝔽8)
commutator, hypocenterC7C3×C313
FrattiniC1G
Fitting, socleC7×C313C3
LCSG ▷ C7
UCSC1 ◁ C313

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1565 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×ΓL(1,𝔽8)×C313, ΓL(1,𝔽8)×D313, AGL(1,𝔽7)×C313, …
maximal normal subgroup ofC2×ΓL(1,𝔽8)×C313, ΓL(1,𝔽8)×D313, AGL(1,𝔽7)×C313, …
maximal quotient ofC2×ΓL(1,𝔽8)×C313, C7⋊C9×C313, C3×ΓL(1,𝔽8)×C313, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6573, 1);