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C2×(C5⋊D5)⋊#3862 #28413444

order14700
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5×C7

Aliases

direct productC2×(C5⋊D5)⋊#3862
unambiguous semidirect product(C2×C5⋊D5)⋊#3862

Splittings

Fitting, socleC2×C52×C72 ⋊ C2×C3
derived, HallC52×C72 ⋊ C22×C3
HallC2×C72×C5⋊D5 ⋊ C3
HallC52⋊#3862 ⋊ C22
HallC2×C5⋊D5 ⋊ #3862
SylowC72 ⋊ C2×(C5⋊D5)⋊C3
SylowC52 ⋊ C22×#3862

Subgroups

subgroupG/H
center, hypercenterC2(C5⋊D5)⋊#3862
commutator, cosocle, hypocenterC52×C72C22×C3
FrattiniC1G
Fitting, socleC2×C52×C72C2×C3
LCSG ▷ C52×C72
UCSC1 ◁ C2

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

468 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 623);