Finite Group Databasebeta

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D9×C25×D37 #45685759

order33300
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productD9×C25×D37
unambiguous semidirect product(D9×C37)⋊(C2×C25)
unambiguous semidirect product(C9×D37)⋊(C2×C25)
unambiguous semidirect productD333⋊(C2×C25)

Splittings

Fitting, HallC9×C25×C37 ⋊ C22
derived, HallC9×C37 ⋊ C22×C25
HallC25×C37 ⋊ C2×D9
HallC9×C25 ⋊ C2×D37
SylowC37 ⋊ C2×D9×C25
SylowC9 ⋊ C2×C25×D37

Subgroups

subgroupG/H
center, hypercenterC25D9×D37
commutator, hypocenterC9×C37C22×C25
FrattiniC3×C5C5×D3×D37
FittingC9×C25×C37C22
socleC3×C5×C37C2×C5×D3
prime radicalC5×D9×D37C5
cosocleC5×C9×C37C22×C5
LCSG ▷ C9×C37
UCSC1 ◁ C25

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8325

Conjugacy classes & character table

3000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 32);