Finite Group Databasebeta

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D3×C49×D25 #28412848

order14700
automorphism?
homologyAbelianization (H1) = C22×C49 · Schur multiplier (H2) = C2

Aliases

direct productD3×C49×D25
unambiguous semidirect product(D3×C25)⋊(C2×C49)
unambiguous semidirect product(C3×D25)⋊(C2×C49)
unambiguous semidirect productD75⋊(C2×C49)

Splittings

Fitting, HallC3×C25×C49 ⋊ C22
derived, HallC3×C25 ⋊ C22×C49
HallC25×C49 ⋊ C2×D3
HallC3×C49 ⋊ C2×D25
SylowC25 ⋊ C2×D3×C49
SylowC3 ⋊ C2×C49×D25

Subgroups

subgroupG/H
center, hypercenterC49D3×D25
commutator, hypocenterC3×C25C22×C49
FrattiniC5×C7D3×C7×D5
FittingC3×C25×C49C22
socleC3×C5×C7C2×C7×D5
prime radicalD3×C7×D25C7
cosocleC3×C7×C25C22×C7
LCSG ▷ C3×C25
UCSC1 ◁ C49

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2058 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 27);