Finite Group Databasebeta

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D3×C7×D7×C25 #28413089

order14700
automorphism?
homologyAbelianization (H1) = C22×C7×C25 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D7×C25
unambiguous semidirect product(D3×C7)⋊(C2×C7×C25)
unambiguous semidirect product(C3×D7)⋊(C2×C7×C25)
unambiguous semidirect productD21⋊(C2×C7×C25)

Splittings

Fitting, HallC3×C72×C25 ⋊ C22
derivedC3×C7 ⋊ C22×C7×C25
HallC72×C25 ⋊ C2×D3
HallC3×C72 ⋊ C22×C25
HallC3×C25 ⋊ C2×C7×D7
SylowC72 ⋊ C2×D3×C25
SylowC3 ⋊ C2×C7×D7×C25

Subgroups

subgroupG/H
center, hypercenterC7×C25D3×D7
commutator, hypocenterC3×C7C22×C7×C25
FrattiniC5C5×D3×C7×D7
FittingC3×C72×C25C22
socleC3×C5×C72C22×C5
prime radicalC5×D3×C7×D7C5
cosocleC3×C5×C7C22×C5×C7
LCSG ▷ C3×C7
UCSC1 ◁ C7×C25

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

normal subgroups only

This group has 156 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

2625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 268);