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C2×C3⋊(C5⋊(C5⋊(C7⋊D7))) #28413574

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

Aliases

direct productC2×C3⋊(C5⋊(C5⋊(C7⋊D7)))
unambiguous semidirect product(C2×C3)⋊(C5⋊(C5⋊(C7⋊D7)))
unambiguous semidirect product(C2×C5)⋊(C3⋊(C5⋊(C7⋊D7)))
unambiguous semidirect product(C2×C7)⋊(C3⋊(C5⋊D35))

Splittings

Fitting, socleC2×C3×C52×C72 ⋊ C2
derived, HallC3×C52×C72 ⋊ C22
HallC52×C72 ⋊ C2×D3
HallC3×C72 ⋊ C2×C5⋊D5
HallC3×C52 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×C3⋊(C5⋊D5)
SylowC52 ⋊ C2×C3⋊(C7⋊D7)
SylowC3 ⋊ C2×C5⋊(C5⋊(C7⋊D7))

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊(C5⋊(C7⋊D7)))
commutator, cosocle, hypocenterC3×C52×C72C22
FrattiniC1G
Fitting, socleC2×C3×C52×C72C2
LCSG ▷ C3×C52×C72
UCSC1 ◁ C2

800 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3678 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 753);