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D41×#63271 #36375603

order22386
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productD41×#63271
unambiguous semidirect productC41⋊(C2×#63271)

Splittings

Fitting, socle, derived, HallC7×C13×C41 ⋊ C2×C3
HallC41×#63271 ⋊ C2
HallC7×C13×D41 ⋊ C3
HallC13×D41 ⋊ ΓL(1,𝔽8)
HallC7×D41 ⋊ C13⋊C3
HallC13×C41 ⋊ C2×ΓL(1,𝔽8)
HallC7×C41 ⋊ C2×C13⋊C3
HallC7×C13 ⋊ C3×D41
SylowC41 ⋊ C2×#63271
SylowC13 ⋊ ΓL(1,𝔽8)×D41
SylowC7 ⋊ C13⋊C3×D41

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C41C2×C3
LCSG ▷ C7×C13×C41
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3731

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22386, 24);