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ΓL(1,𝔽8)×D851 #49088367

order35742
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D851
unambiguous semidirect productC23⋊(ΓL(1,𝔽8)×D37)

Splittings

Fitting, socle, derived, HallC7×C23×C37 ⋊ C2×C3
HallΓL(1,𝔽8)×C23×C37 ⋊ C2
HallC7×D851 ⋊ C3
HallC23×C37 ⋊ C2×ΓL(1,𝔽8)
HallΓL(1,𝔽8)×C37 ⋊ D23
HallΓL(1,𝔽8)×C23 ⋊ D37
HallC7×C37 ⋊ C3×D23
HallC7×C23 ⋊ C3×D37
SylowC37 ⋊ ΓL(1,𝔽8)×D23
SylowC23 ⋊ ΓL(1,𝔽8)×D37
SylowC7 ⋊ C3×D851

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C23×C37C2×C3
LCSG ▷ C7×C23×C37
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5957

Conjugacy classes & character table

2135 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35742, 30);