Finite Group Databasebeta

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C2×C31×D225 #42124307

order27900
isoclinismisoclinic class of D225
automorphism?
homologyAbelianization (H1) = C22×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C31×D225
unambiguous semidirect product(C2×C9)⋊(C31×D25)
unambiguous semidirect product(C2×C25)⋊(D9×C31)

Splittings

FittingC2×C9×C25×C31 ⋊ C2
derived, HallC9×C25 ⋊ C22×C31
HallC9×C25×C31 ⋊ C22
HallC25×C31 ⋊ C2×D9
HallC9×C31 ⋊ C2×D25
SylowC25 ⋊ C2×D9×C31
SylowC9 ⋊ C2×C31×D25

Subgroups

subgroupG/H
center, hypercenterC2×C31D225
commutator, cosocle, hypocenterC9×C25C22×C31
FrattiniC3×C5C2×D15×C31
FittingC2×C9×C25×C31C2
socleC2×C3×C5×C31D15
LCSG ▷ C9×C25
UCSC1 ◁ C2×C31

90 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, 54);