Finite Group Databasebeta

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C4×C37×C73⋊C3 #44569399

order32412
automorphism?
homologyAbelianization (H1) = C3×C4×C37 · Schur multiplier (H2) = C1

Aliases

direct productC4×C37×C73⋊C3
unambiguous semidirect product(C4×C73)⋊(C3×C37)

Splittings

Fitting, HallC4×C37×C73 ⋊ C3
derived, SylowC73 ⋊ C3×C4×C37
HallC37×C73 ⋊ C3×C4
HallC4×C73 ⋊ C3×C37

Subgroups

subgroupG/H
center, hypercenterC4×C37C73⋊C3
commutator, hypocenterC73C3×C4×C37
FrattiniC2C2×C37×C73⋊C3
FittingC4×C37×C73C3
socleC2×C37×C73C2×C3
prime radicalC2×C37×C73⋊C3C2
cosocleC2×C73C2×C3×C37
LCSG ▷ C73
UCSC1 ◁ C4×C37

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10804

Conjugacy classes & character table

3996 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32412, 2);