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C2×C49×(C5⋊D5)⋊C3 #28412957

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

Aliases

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

Splittings

FittingC2×C52×C49 ⋊ C2×C3
derived, SylowC52 ⋊ C22×C3×C49
HallC2×C49×C5⋊D5 ⋊ C3
HallC49×C52⋊C3 ⋊ C22
HallC52×C49 ⋊ C22×C3
HallC2×C5⋊D5 ⋊ C3×C49
HallC52⋊C3 ⋊ C22×C49

Subgroups

subgroupG/H
center, hypercenterC2×C49(C5⋊D5)⋊C3
commutator, hypocenterC52C22×C3×C49
FrattiniC7C2×C7×(C5⋊D5)⋊C3
FittingC2×C52×C49C2×C3
socleC2×C52×C7C2×C3×C7
prime radicalC2×C7×(C5⋊D5)⋊C3C7
cosocleC52×C7C22×C3×C7
LCSG ▷ C52
UCSC1 ◁ C2×C49

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

980 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 136);