Finite Group Databasebeta

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C2×C9×C31×D25 #42124303

order27900
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C22×C9×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C31×D25
unambiguous semidirect productC25⋊(C22×C9×C31)
unambiguous semidirect product(C2×C25)⋊(C2×C9×C31)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C9×C31D25
commutator, hypocenterC25C22×C9×C31
FrattiniC3×C5C2×C3×D5×C31
FittingC2×C9×C25×C31C2
socleC2×C3×C5×C31C3×D5
prime radicalC2×C3×C31×D25C3
cosocleC3×C25C22×C3×C31
LCSG ▷ C25
UCSC1 ◁ C2×C9×C31

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7812 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 50);