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ΓL(1,𝔽8)×C37×D23 #49088363

order35742
automorphism?
homologyAbelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C37×D23
unambiguous semidirect productC23⋊(C2×ΓL(1,𝔽8)×C37)
unambiguous semidirect product(C7×D23)⋊(C3×C37)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC37ΓL(1,𝔽8)×D23
commutator, cosocle, hypocenterC7×C23C2×C3×C37
FrattiniC1G
Fitting, socleC7×C23×C37C2×C3
LCSG ▷ C7×C23
UCSC1 ◁ C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5957

Conjugacy classes & character table

2405 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35742, 26);