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C5×C41⋊(D7⋊C9) #38788925

order25830
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C41⋊(D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(C5×D41)
unambiguous semidirect product(C5×D287)⋊C9

Splittings

derived, HallC7×C41 ⋊ C2×C5×C9
HallC5×C41×C7⋊C9 ⋊ C2
HallC5×D287 ⋊ C9
HallC41×C7⋊C9 ⋊ C2×C5
HallC5×C7×C41 ⋊ C2×C9
HallD287 ⋊ C5×C9
HallC5×C7⋊C9 ⋊ D41
HallC5×C41 ⋊ D7⋊C9
HallC7⋊C9 ⋊ C5×D41
SylowC41 ⋊ C5×D7⋊C9
HallC5×C7 ⋊ C9×D41
SylowC7 ⋊ C5×C9×D41

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊D41
commutator, hypocenterC7×C41C2×C5×C9
FrattiniC3C5×ΓL(1,𝔽8)⋊D41
Fitting, socleC3×C5×C7×C41C2×C3
prime radicalC3×C5×D287C3
cosocleC3×C7×C41C2×C3×C5
LCSG ▷ C7×C41
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12915

Conjugacy classes & character table

1605 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 29);