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C41×(C13⋊C3)⋊D7 #36375620

order22386
automorphism?
homologyAbelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×(C13⋊C3)⋊D7
unambiguous semidirect product(C13⋊C3)⋊(D7×C41)

Splittings

Fitting, socle, HallC7×C13×C41 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C41
HallC7×C13⋊C3×C41 ⋊ C2
HallC41×D91 ⋊ C3
HallC13⋊C3×C41 ⋊ D7
HallC13×C41 ⋊ C3×D7
HallC7×C41 ⋊ D13⋊C3
HallC7×C13⋊C3 ⋊ C2×C41
HallD91 ⋊ C3×C41
HallC13⋊C3 ⋊ D7×C41
SylowC13 ⋊ C3×D7×C41
SylowC7 ⋊ C41×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC41(C13⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C13C2×C3×C41
FrattiniC1G
Fitting, socleC7×C13×C41C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3731

Conjugacy classes & character table

1189 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22386, 41);