Finite Group Databasebeta

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C5×D3×D5×C49 #28412980

order14700
automorphism?
homologyAbelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×D5×C49
unambiguous semidirect product(C5×D3)⋊(C2×C5×C49)
unambiguous semidirect product(C3×D5)⋊(C2×C5×C49)
unambiguous semidirect productD15⋊(C2×C5×C49)

Splittings

Fitting, HallC3×C52×C49 ⋊ C22
derivedC3×C5 ⋊ C22×C5×C49
HallC52×C49 ⋊ C2×D3
HallC3×C49 ⋊ C2×C5×D5
HallC3×C52 ⋊ C22×C49
SylowC52 ⋊ C2×D3×C49
SylowC3 ⋊ C2×C5×D5×C49

Subgroups

subgroupG/H
center, hypercenterC5×C49D3×D5
commutator, hypocenterC3×C5C22×C5×C49
FrattiniC7C5×D3×C7×D5
FittingC3×C52×C49C22
socleC3×C52×C7C22×C7
prime radicalC5×D3×C7×D5C7
cosocleC3×C5×C7C22×C5×C7
LCSG ▷ C3×C5
UCSC1 ◁ C5×C49

144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 159);