Finite Group Databasebeta

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C5×C7×D15⋊D7 #28413508

order14700
isoclinismisoclinic class of D15⋊D7
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×D15⋊D7
unambiguous semidirect productD15⋊(C5×C7×D7)
unambiguous semidirect productD21⋊(C5×C7×D5)
unambiguous semidirect productD35⋊(C5×D3×C7)

Splittings

Fitting, socle, HallC3×C52×C72 ⋊ C22
derivedC3×C5×C7 ⋊ C22×C5×C7
HallC52×C72 ⋊ C2×D3
HallC3×C72 ⋊ C2×C5×D5
HallC3×C52 ⋊ C2×C7×D7
SylowC72 ⋊ C5×D3×D5
SylowC52 ⋊ D3×C7×D7
SylowC3 ⋊ C5×C7×D5×D7

Subgroups

subgroupG/H
center, hypercenterC5×C7D15⋊D7
commutator, cosocle, hypocenterC3×C5×C7C22×C5×C7
FrattiniC1G
Fitting, socleC3×C52×C72C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C5×C7

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

normal subgroups only

This group has 252 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

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 687);