Finite Group Databasebeta

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C2×C3×C5×D5×C49 #28413010

order14700
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D5×C49
unambiguous semidirect productC5⋊(C22×C3×C5×C49)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C5×C49)

Splittings

FittingC2×C3×C52×C49 ⋊ C2
derivedC5 ⋊ C22×C3×C5×C49
HallC3×C52×C49 ⋊ C22
HallC52×C49 ⋊ C22×C3
HallC3×C52 ⋊ C22×C49
SylowC52 ⋊ C22×C3×C49

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C49D5
commutator, hypocenterC5C22×C3×C5×C49
FrattiniC7C2×C3×C5×C7×D5
FittingC2×C3×C52×C49C2
socleC2×C3×C52×C7C2×C7
prime radicalC2×C3×C5×C7×D5C7
cosocleC5×C7C22×C3×C5×C7
LCSG ▷ C5
UCSC1 ◁ C2×C3×C5×C49

144 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 84 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

5880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 189);