Finite Group Databasebeta

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C32×C5×D5×C49 #36347698

order22050
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C49 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×D5×C49
unambiguous semidirect productC5⋊(C2×C32×C5×C49)

Splittings

Fitting, HallC32×C52×C49 ⋊ C2
derivedC5 ⋊ C2×C32×C5×C49
HallC52×C49 ⋊ C2×C32
HallC32×C52 ⋊ C2×C49
SylowC52 ⋊ C2×C32×C49

Subgroups

subgroupG/H
center, hypercenterC32×C5×C49D5
commutator, hypocenterC5C2×C32×C5×C49
FrattiniC7C32×C5×C7×D5
FittingC32×C52×C49C2
socleC32×C52×C7C2×C7
prime radicalC32×C5×C7×D5C7
cosocleC5×C7C2×C32×C5×C7
LCSG ▷ C5
UCSC1 ◁ C32×C5×C49

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4410

Conjugacy classes & character table

8820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 135);