Finite Group Databasebeta

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C2×C25×D109⋊C3 #45658185

order32700
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×D109⋊C3
unambiguous semidirect productD109⋊(C2×C3×C25)
unambiguous semidirect product(C109⋊C3)⋊(C22×C25)
unambiguous semidirect product(C2×D109)⋊(C3×C25)
unambiguous semidirect product(C2×C109⋊C3)⋊(C2×C25)
unambiguous semidirect product(C2×C25×D109)⋊C3

Splittings

FittingC2×C25×C109 ⋊ C2×C3
derived, SylowC109 ⋊ C22×C3×C25
HallC2×C25×D109 ⋊ C3
HallC25×C109⋊C3 ⋊ C22
HallC25×C109 ⋊ C22×C3
HallC2×D109 ⋊ C3×C25
HallC109⋊C3 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25D109⋊C3
commutator, hypocenterC109C22×C3×C25
FrattiniC5C2×C5×D109⋊C3
FittingC2×C25×C109C2×C3
socleC2×C5×C109C2×C3×C5
prime radicalC2×C5×D109⋊C3C5
cosocleC5×C109C22×C3×C5
LCSG ▷ C109
UCSC1 ◁ C2×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5450

Conjugacy classes & character table

1200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 21);