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ΓL(1,𝔽8)×C421 #22579580

order8841
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C421 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C421
unambiguous semidirect productC7⋊(C3×C421)

Splittings

Fitting, socle, HallC7×C421 ⋊ C3
derived, SylowC7 ⋊ C3×C421

Subgroups

subgroupG/H
center, hypercenterC421ΓL(1,𝔽8)
commutator, hypocenterC7C3×C421
FrattiniC1G
Fitting, socleC7×C421C3
LCSG ▷ C7
UCSC1 ◁ C421

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2105 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×ΓL(1,𝔽8)×C421, ΓL(1,𝔽8)×D421, AGL(1,𝔽7)×C421, …
maximal normal subgroup ofC2×ΓL(1,𝔽8)×C421, ΓL(1,𝔽8)×D421, AGL(1,𝔽7)×C421, …
maximal quotient ofC2×ΓL(1,𝔽8)×C421, C7⋊C9×C421, C3×ΓL(1,𝔽8)×C421, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8841, 3);