Finite Group Databasebeta

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C2×C49×D75 #28412860

order14700
isoclinismisoclinic class of D75
automorphism?
homologyAbelianization (H1) = C22×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C49×D75
unambiguous semidirect product(C2×C3)⋊(C49×D25)
unambiguous semidirect product(C2×C25)⋊(D3×C49)

Splittings

FittingC2×C3×C25×C49 ⋊ C2
derived, HallC3×C25 ⋊ C22×C49
HallC3×C25×C49 ⋊ C22
HallC25×C49 ⋊ C2×D3
HallC3×C49 ⋊ C2×D25
SylowC25 ⋊ C2×D3×C49
SylowC3 ⋊ C2×C49×D25

Subgroups

subgroupG/H
center, hypercenterC2×C49D75
commutator, hypocenterC3×C25C22×C49
FrattiniC5×C7C2×C7×D15
FittingC2×C3×C25×C49C2
socleC2×C3×C5×C7C7×D5
prime radicalC2×C7×D75C7
cosocleC3×C7×C25C22×C7
LCSG ▷ C3×C25
UCSC1 ◁ C2×C49

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3822 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 39);