Finite Group Databasebeta

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C32×C5×Dic121 #36344697

order21780
isoclinismisoclinic class of D121
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×Dic121

Splittings

derived, SylowC121 ⋊ C32×C4×C5
HallC32×C5×C121 ⋊ C4
HallC32×C121 ⋊ C4×C5
HallC5×C121 ⋊ C32×C4

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D121
commutator, hypocenterC121C32×C4×C5
FrattiniC2×C11C32×C5×D11
FittingC2×C32×C5×C121C2
socle, prime radicalC2×C32×C5×C11D11
cosocleC2×C121C2×C32×C5
LCSG ▷ C121
UCSC1 ◁ C2×C32×C5

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 46);