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ΓL(1,𝔽8)×#13133724 #49088991

order35805
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×#13133724
unambiguous semidirect productC7⋊(C3×#13133724)

Splittings

Fitting, socle, derived, HallC7×C11×C31 ⋊ C3×C5
HallC7×#13133724 ⋊ C3
HallC11×ΓL(1,𝔽8)×C31 ⋊ C5
HallΓL(1,𝔽8)×C31 ⋊ C11⋊C5
HallC11×C31 ⋊ C5×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ ΓL(1,𝔽32)
HallC7×C31 ⋊ C3×C11⋊C5
HallC7×C11 ⋊ C3×ΓL(1,𝔽32)
SylowC31 ⋊ ΓL(1,𝔽8)×C11⋊C5
SylowC11 ⋊ ΓL(1,𝔽8)×ΓL(1,𝔽32)
SylowC7 ⋊ C3×#13133724

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C31C3×C5
LCSG ▷ C7×C11×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35805, 23);