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ΓL(1,𝔽8)×C7⋊#595 #23756198

order9996
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C7⋊#595

Splittings

Fitting, socle, derived, HallC72×C17 ⋊ C3×C4
HallC7×C7⋊#595 ⋊ C3
HallC7×C17×ΓL(1,𝔽8) ⋊ C4
HallC7×ΓL(1,𝔽8) ⋊ #595
SylowC72 ⋊ C3×#595
SylowC17 ⋊ ΓL(1,𝔽8)×Dic7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC72×C17C3×C4
prime radicalC7×ΓL(1,𝔽8)×D17C2
cosocleC72×D17C2×C3
LCSG ▷ C72×C17
UCSC1

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×ΓL(1,𝔽8)⋊#595, C3×ΓL(1,𝔽8)×C7⋊#595, ΓL(1,𝔽8)×C3⋊(C7⋊#595)
maximal normal subgroup ofΓL(1,𝔽8)×ΓL(1,𝔽8)⋊#595, C3×ΓL(1,𝔽8)×C7⋊#595
maximal quotient ofC7⋊C9×C7⋊#595, C3×ΓL(1,𝔽8)×C7⋊#595, ΓL(1,𝔽8)×C3⋊(C7⋊#595)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9996, 101);