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C41×D49⋊C9 #49116261

order36162
automorphism?
homologyAbelianization (H1) = C2×C9×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×D49⋊C9
unambiguous semidirect productD49⋊(C9×C41)
unambiguous semidirect product(C49⋊C9)⋊(C2×C41)
unambiguous semidirect product(C41×D49)⋊C9

Splittings

derived, SylowC49 ⋊ C2×C9×C41
HallC41×C49⋊C9 ⋊ C2
HallC41×D49 ⋊ C9
HallC41×C49 ⋊ C2×C9
HallC49⋊C9 ⋊ C2×C41
HallD49 ⋊ C9×C41

Subgroups

subgroupG/H
center, hypercenterC3×C41D49⋊C3
commutator, hypocenterC49C2×C9×C41
FrattiniC3×C7C41×AGL(1,𝔽7)
FittingC3×C41×C49C2×C3
socleC3×C7×C41AGL(1,𝔽7)
prime radicalC3×C41×D49C3
cosocleC3×C49C2×C3×C41
LCSG ▷ C49
UCSC1 ◁ C3×C41

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18081

Conjugacy classes & character table

1722 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36162, 3);