Finite Group Databasebeta

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C5×C47⋊(D7⋊C9) #44444083

order29610
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C47⋊(D7⋊C9)
unambiguous semidirect productC47⋊(C5×D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(C5×D47)
unambiguous semidirect productD329⋊(C5×C9)
unambiguous semidirect product(C5×D329)⋊C9

Splittings

derived, HallC7×C47 ⋊ C2×C5×C9
HallC5×C47×C7⋊C9 ⋊ C2
HallC5×D329 ⋊ C9
HallC47×C7⋊C9 ⋊ C2×C5
HallC5×C7×C47 ⋊ C2×C9
HallD329 ⋊ C5×C9
HallC5×C7⋊C9 ⋊ D47
HallC5×C47 ⋊ D7⋊C9
HallC7⋊C9 ⋊ C5×D47
SylowC47 ⋊ C5×D7⋊C9
HallC5×C7 ⋊ C9×D47
SylowC7 ⋊ C5×C9×D47

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊D47
commutator, hypocenterC7×C47C2×C5×C9
FrattiniC3C5×ΓL(1,𝔽8)⋊D47
Fitting, socleC3×C5×C7×C47C2×C3
prime radicalC3×C5×D329C3
cosocleC3×C7×C47C2×C3×C5
LCSG ▷ C7×C47
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14805

Conjugacy classes & character table

1830 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 20);