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C5×ΓL(1,𝔽8)×C67 #20296368

order7035
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C5×C67 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×C67
unambiguous semidirect productC7⋊(C3×C5×C67)
unambiguous semidirect product(C5×C7)⋊(C3×C67)

Splittings

Fitting, socle, HallC5×C7×C67 ⋊ C3
derived, SylowC7 ⋊ C3×C5×C67
HallC7×C67 ⋊ C3×C5
HallC5×C7 ⋊ C3×C67

Subgroups

subgroupG/H
center, hypercenterC5×C67ΓL(1,𝔽8)
commutator, hypocenterC7C3×C5×C67
FrattiniC1G
Fitting, socleC5×C7×C67C3
LCSG ▷ C7
UCSC1 ◁ C5×C67

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1675 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×ΓL(1,𝔽8)×C67, C5×ΓL(1,𝔽8)×D67, C5×AGL(1,𝔽7)×C67, …
maximal normal subgroup ofC2×C5×ΓL(1,𝔽8)×C67, C5×ΓL(1,𝔽8)×D67, C5×AGL(1,𝔽7)×C67, …
maximal quotient ofC2×C5×ΓL(1,𝔽8)×C67, C5×C7⋊C9×C67, C3×C5×ΓL(1,𝔽8)×C67, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7035, 3);