Finite Group Databasebeta

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C2×C9×D5×C121 #36344684

order21780
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C9×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D5×C121
unambiguous semidirect productC5⋊(C22×C9×C121)
unambiguous semidirect product(C2×C5)⋊(C2×C9×C121)

Splittings

FittingC2×C5×C9×C121 ⋊ C2
derived, SylowC5 ⋊ C22×C9×C121
HallC5×C9×C121 ⋊ C22
HallC5×C121 ⋊ C22×C9
HallC5×C9 ⋊ C22×C121

Subgroups

subgroupG/H
center, hypercenterC2×C9×C121D5
commutator, hypocenterC5C22×C9×C121
FrattiniC3×C11C2×C3×D5×C11
FittingC2×C5×C9×C121C2
socleC2×C3×C5×C11C2×C3×C11
prime radicalC2×C3×D5×C11C3×C11
cosocleC3×C5×C11C22×C3×C11
LCSG ▷ C5
UCSC1 ◁ C2×C9×C121

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 33);