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C3×ΓL(1,𝔽8)×D73 #22604126

order9198
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×D73

Splittings

Fitting, socleC3×C7×C73 ⋊ C2×C3
derived, HallC7×C73 ⋊ C2×C32
HallC3×ΓL(1,𝔽8)×C73 ⋊ C2
HallC7×D73 ⋊ C32
SylowC73 ⋊ C2×C3×ΓL(1,𝔽8)
SylowC7 ⋊ C32×D73

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×D73
commutator, hypocenterC7×C73C2×C32
FrattiniC1G
Fitting, socleC3×C7×C73C2×C3
LCSG ▷ C7×C73
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×ΓL(1,𝔽8)⋊#64408, C3×AGL(1,𝔽7)×D73, C3×ΓL(1,𝔽8)×#64408, …
maximal normal subgroup ofC3×ΓL(1,𝔽8)⋊#64408, C3×AGL(1,𝔽7)×D73, C3×ΓL(1,𝔽8)×#64408, …
maximal quotient ofC3×ΓL(1,𝔽8)×Dic73, C2×C3×ΓL(1,𝔽8)×D73

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9198, 51);