Finite Group Databasebeta

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C32×C49×#261 #37524268

order22932
automorphism?
homologyAbelianization (H1) = C32×C4×C49 · Schur multiplier (H2) = C3

Aliases

direct productC32×C49×#261

Splittings

Fitting, HallC32×C13×C49 ⋊ C4
derived, SylowC13 ⋊ C32×C4×C49
HallC13×C49 ⋊ C32×C4
HallC32×C13 ⋊ C4×C49

Subgroups

subgroupG/H
center, hypercenterC32×C49#261
commutator, hypocenterC13C32×C4×C49
FrattiniC7C32×C7×#261
FittingC32×C13×C49C4
socleC32×C7×C13C4×C7
prime radicalC32×C7×D13C2×C7
cosocleC7×D13C2×C32×C7
LCSG ▷ C13
UCSC1 ◁ C32×C49

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5733

Conjugacy classes & character table

3087 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 213);