Finite Group Databasebeta

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D5×C31×C7⋊C9 #34086141

order19530
automorphism?
homologyAbelianization (H1) = C2×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productD5×C31×C7⋊C9
unambiguous semidirect productC5⋊(C2×C31×C7⋊C9)
unambiguous semidirect product(C7×D5)⋊(C9×C31)

Splittings

derived, HallC5×C7 ⋊ C2×C9×C31
HallC5×C31×C7⋊C9 ⋊ C2
HallC7×D5×C31 ⋊ C9
HallC5×C7×C31 ⋊ C2×C9
HallC5×C7⋊C9 ⋊ C2×C31
HallC7×C31 ⋊ C9×D5
HallC5×C31 ⋊ C2×C7⋊C9
HallC7×D5 ⋊ C9×C31
SylowC7 ⋊ C9×D5×C31
SylowC5 ⋊ C2×C31×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C31D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C2×C9×C31
FrattiniC3D5×ΓL(1,𝔽8)×C31
Fitting, socleC3×C5×C7×C31C2×C3
prime radicalC3×C7×D5×C31C3
cosocleC3×C5×C7C2×C3×C31
LCSG ▷ C5×C7
UCSC1 ◁ C3×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9765

Conjugacy classes & character table

1860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 46);