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C41×D357 #44418082

order29274
automorphism?
homologyAbelianization (H1) = C2×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×D357
unambiguous semidirect productC3⋊(C41×D119)
unambiguous semidirect productC7⋊(C41×D51)
unambiguous semidirect productC17⋊(C41×D21)

Splittings

Fitting, socle, HallC3×C7×C17×C41 ⋊ C2
derived, HallC3×C7×C17 ⋊ C2×C41
HallC7×C17×C41 ⋊ D3
HallC3×C17×C41 ⋊ D7
HallC3×C7×C41 ⋊ D17
HallC17×C41 ⋊ D21
HallC7×C41 ⋊ D51
HallC3×C41 ⋊ D119
HallC7×C17 ⋊ D3×C41
HallC3×C17 ⋊ D7×C41
HallC3×C7 ⋊ D17×C41
SylowC17 ⋊ C41×D21
SylowC7 ⋊ C41×D51
SylowC3 ⋊ C41×D119

Subgroups

subgroupG/H
center, hypercenterC41D357
commutator, cosocle, hypocenterC3×C7×C17C2×C41
FrattiniC1G
Fitting, socleC3×C7×C17×C41C2
LCSG ▷ C3×C7×C17
UCSC1 ◁ C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14637

Conjugacy classes & character table

7380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29274, 16);