Finite Group Databasebeta

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C2×C31×C5⋊D45 #42124583

order27900
isoclinismisoclinic class of C5⋊D45
automorphism?
homologyAbelianization (H1) = C22×C31 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C31×C5⋊D45
unambiguous semidirect product(C2×C5)⋊(C31×D45)
unambiguous semidirect product(C2×C9)⋊(C31×C5⋊D5)

Splittings

FittingC2×C52×C9×C31 ⋊ C2
derived, HallC52×C9 ⋊ C22×C31
HallC52×C9×C31 ⋊ C22
HallC52×C31 ⋊ C2×D9
HallC9×C31 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×D9×C31
SylowC9 ⋊ C2×C31×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C31C5⋊D45
commutator, cosocle, hypocenterC52×C9C22×C31
FrattiniC3C2×C31×C3⋊(C5⋊D5)
FittingC2×C52×C9×C31C2
socleC2×C3×C52×C31D3
LCSG ▷ C52×C9
UCSC1 ◁ C2×C31

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 330);