Finite Group Databasebeta

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C25×C22⋊(C109⋊C3) #45658209

order32700
automorphism?
homologyAbelianization (H1) = C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC25×C22⋊(C109⋊C3)
unambiguous semidirect productC22⋊(C25×C109⋊C3)
unambiguous semidirect product(C22×C25)⋊(C109⋊C3)
unambiguous semidirect productC109⋊(A4×C25)
unambiguous semidirect product(C25×C109)⋊A4

Splittings

Fitting, HallC22×C25×C109 ⋊ C3
derived, HallC22×C109 ⋊ C3×C25
HallC25×C109 ⋊ A4
SylowC109 ⋊ A4×C25
HallC22×C25 ⋊ C109⋊C3
SylowC22 ⋊ C25×C109⋊C3

Subgroups

subgroupG/H
center, hypercenterC25C22⋊(C109⋊C3)
commutator, hypocenterC22×C109C3×C25
FrattiniC5C5×C22⋊(C109⋊C3)
FittingC22×C25×C109C3
socle, cosocleC22×C5×C109C3×C5
prime radicalC5×C22⋊(C109⋊C3)C5
LCSG ▷ C22×C109
UCSC1 ◁ C25

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10900

Conjugacy classes & character table

3700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 45);