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C2×C3⋊(C3⋊(C5⋊D35)) #20263156

order6300
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C3⋊(C3⋊(C5⋊D35))
unambiguous semidirect product(C2×C3)⋊(C3⋊(C5⋊D35))
unambiguous semidirect product(C2×C5)⋊(C3⋊D105)
unambiguous semidirect product(C2×C7)⋊(C3⋊(C3⋊(C5⋊D5)))

Splittings

Fitting, socleC2×C32×C52×C7 ⋊ C2
derived, HallC32×C52×C7 ⋊ C22
HallC32×C52 ⋊ C2×D7
HallC52×C7 ⋊ C2×C3⋊D3
HallC32×C7 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×C3⋊D21
SylowC32 ⋊ C2×C5⋊D35
SylowC7 ⋊ C2×C3⋊(C3⋊(C5⋊D5))

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C3⋊(C5⋊D35))
commutator, hypocenterC32×C52×C7C22
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C32×C52×C7
UCSC1 ◁ C2

480 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1578 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6300, 552);