Finite Group Databasebeta

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C2×C5×D9×C31 #19150063

order5580
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C22×C5×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D9×C31
unambiguous semidirect productC9⋊(C22×C5×C31)
unambiguous semidirect product(C2×C9)⋊(C2×C5×C31)

Splittings

FittingC2×C5×C9×C31 ⋊ C2
derived, SylowC9 ⋊ C22×C5×C31
HallC5×C9×C31 ⋊ C22
HallC9×C31 ⋊ C22×C5
HallC5×C9 ⋊ C22×C31

Subgroups

subgroupG/H
center, hypercenterC2×C5×C31D9
commutator, hypocenterC9C22×C5×C31
FrattiniC3C2×C5×D3×C31
FittingC2×C5×C9×C31C2
socleC2×C3×C5×C31D3
LCSG ▷ C9
UCSC1 ◁ C2×C5×C31

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×D9×C31⋊C25, C2×D9×C25×C31, C2×C5×D9×ΓL(1,𝔽32), …
maximal normal subgroup ofC2×D9×C31⋊C25, C2×D9×C25×C31, C2×C5×D9×ΓL(1,𝔽32), …
maximal quotient ofC2×D9×C25×C31, C5×D5×D9×C31, C2×C5×C31×D45, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 52);