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C2×C5⋊(C5⋊(C7⋊D7)) #19096701

order4900
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C5×C7

Aliases

direct productC2×C5⋊(C5⋊(C7⋊D7))
unambiguous semidirect product(C2×C5)⋊(C5⋊(C7⋊D7))
unambiguous semidirect product(C2×C7)⋊(C5⋊D35)

Splittings

Fitting, socleC2×C52×C72 ⋊ C2
derived, HallC52×C72 ⋊ C22
SylowC72 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C5⋊(C7⋊D7))
commutator, hypocenterC52×C72C22
FrattiniC1G
Fitting, socleC2×C52×C72C2
LCSG ▷ C52×C72
UCSC1 ◁ C2

400 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊(C5⋊#64424), C2×C5⋊(C5⋊#64425), C2×C5⋊(C5⋊(ΓL(1,𝔽8)⋊D7)), …
maximal normal subgroup ofC2×C5⋊(C5⋊#64424), C2×C5⋊(C5⋊#64425), C2×C5⋊(C5⋊(ΓL(1,𝔽8)⋊D7)), …
maximal quotient ofD3×C5⋊(C5⋊(C7⋊D7)), C2×C3⋊(C5⋊(C5⋊(C7⋊D7))), C2×C3×C5⋊(C5⋊(C7⋊D7))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4900, 105);