Finite Group Databasebeta

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C2×C3⋊(C3⋊(C5⋊D155)) #42124996

order27900
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C3⋊(C3⋊(C5⋊D155))
unambiguous semidirect product(C2×C3)⋊(C3⋊(C5⋊D155))
unambiguous semidirect product(C2×C5)⋊(C3⋊D465)
unambiguous semidirect product(C2×C31)⋊(C3⋊(C3⋊(C5⋊D5)))

Splittings

Fitting, socleC2×C32×C52×C31 ⋊ C2
derived, HallC32×C52×C31 ⋊ C22
HallC52×C31 ⋊ C2×C3⋊D3
HallC32×C31 ⋊ C2×C5⋊D5
HallC32×C52 ⋊ C2×D31
SylowC31 ⋊ C2×C3⋊(C3⋊(C5⋊D5))
SylowC52 ⋊ C2×C3⋊D93
SylowC32 ⋊ C2×C5⋊D155

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C3⋊(C5⋊D155))
commutator, cosocle, hypocenterC32×C52×C31C22
FrattiniC1G
Fitting, socleC2×C32×C52×C31C2
LCSG ▷ C32×C52×C31
UCSC1 ◁ C2

480 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6978 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 743);