Finite Group Databasebeta

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C32×C7×C5⋊D55 #46831659

order34650
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3×C5

Aliases

direct productC32×C7×C5⋊D55
unambiguous semidirect productC5⋊(C32×C7×D55)
unambiguous semidirect productC11⋊(C32×C7×C5⋊D5)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derived, HallC52×C11 ⋊ C2×C32×C7
HallC32×C52×C11 ⋊ C2×C7
HallC52×C7×C11 ⋊ C2×C32
HallC32×C52×C7 ⋊ D11
HallC32×C7×C11 ⋊ C5⋊D5
HallC32×C52 ⋊ C7×D11
HallC52×C7 ⋊ C32×D11
HallC32×C11 ⋊ C7×C5⋊D5
HallC7×C11 ⋊ C32×C5⋊D5
SylowC52 ⋊ C32×C7×D11
SylowC11 ⋊ C32×C7×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC32×C7C5⋊D55
commutator, cosocle, hypocenterC52×C11C2×C32×C7
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C52×C11
UCSC1 ◁ C32×C7

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

8757 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 302);