Finite Group Databasebeta

C5×C41×D7⋊C9 #38788924

order25830
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C41 · Schur multiplier (H2) = C1

Aliases

direct productC5×C41×D7⋊C9
unambiguous semidirect productD7⋊(C5×C9×C41)
unambiguous semidirect product(C7⋊C9)⋊(C2×C5×C41)
unambiguous semidirect product(C5×D7)⋊(C9×C41)
unambiguous semidirect product(C5×D7×C41)⋊C9

Splittings

derived, SylowC7 ⋊ C2×C5×C9×C41
HallC5×C41×C7⋊C9 ⋊ C2
HallC5×D7×C41 ⋊ C9
HallC41×C7⋊C9 ⋊ C2×C5
HallC5×C7×C41 ⋊ C2×C9
HallD7×C41 ⋊ C5×C9
HallC5×C7⋊C9 ⋊ C2×C41
HallC7×C41 ⋊ C2×C5×C9
HallC5×D7 ⋊ C9×C41
HallC7⋊C9 ⋊ C2×C5×C41
HallC5×C7 ⋊ C2×C9×C41
HallD7 ⋊ C5×C9×C41

Subgroups

subgroupG/H
center, hypercenterC3×C5×C41AGL(1,𝔽7)
commutator, hypocenterC7C2×C5×C9×C41
FrattiniC3C5×C41×AGL(1,𝔽7)
Fitting, socleC3×C5×C7×C41C2×C3
prime radicalC3×C5×D7×C41C3
cosocleC3×C7C2×C3×C5×C41
LCSG ▷ C7
UCSC1 ◁ C3×C5×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12915

Conjugacy classes & character table

4305 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 28);