Finite Group Databasebeta

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D3×C25×D49 #28412846

order14700
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productD3×C25×D49
unambiguous semidirect product(D3×C49)⋊(C2×C25)
unambiguous semidirect product(C3×D49)⋊(C2×C25)
unambiguous semidirect productD147⋊(C2×C25)

Splittings

Fitting, HallC3×C25×C49 ⋊ C22
derived, HallC3×C49 ⋊ C22×C25
HallC25×C49 ⋊ C2×D3
HallC3×C25 ⋊ C2×D49
SylowC49 ⋊ C2×D3×C25
SylowC3 ⋊ C2×C25×D49

Subgroups

subgroupG/H
center, hypercenterC25D3×D49
commutator, hypocenterC3×C49C22×C25
FrattiniC5×C7C5×D3×D7
FittingC3×C25×C49C22
socleC3×C5×C7C2×C5×D7
prime radicalC5×D3×D49C5
cosocleC3×C5×C49C22×C5
LCSG ▷ C3×C49
UCSC1 ◁ C25

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 25);