Finite Group Databasebeta

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C25×C22⋊#66524 #45685772

order33300
automorphism?
homologyAbelianization (H1) = C9×C25 · Schur multiplier (H2) = C2

Aliases

direct productC25×C22⋊#66524
unambiguous semidirect productC22⋊(C25×#66524)
unambiguous semidirect product(C22×C25)⋊#66524

Splittings

derived, HallC22×C37 ⋊ C9×C25
HallC22×C25×C37 ⋊ C9
HallC25×C37 ⋊ C22⋊C9
HallC22×C25 ⋊ #66524
SylowC37 ⋊ C25×C22⋊C9
SylowC22 ⋊ C25×#66524

Subgroups

subgroupG/H
center, hypercenterC3×C25C22⋊(C37⋊C3)
commutator, hypocenterC22×C37C9×C25
FrattiniC3×C5C5×C22⋊(C37⋊C3)
FittingC22×C3×C25×C37C3
socle, prime radical, cosocleC22×C3×C5×C37C3×C5
LCSG ▷ C22×C37
UCSC1 ◁ C3×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16650

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 45);