Finite Group Databasebeta

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C52×C11×C3⋊D21 #46831676

order34650
automorphism?
homologyAbelianization (H1) = C2×C52×C11 · Schur multiplier (H2) = C3×C5

Aliases

direct productC52×C11×C3⋊D21
unambiguous semidirect productC3⋊(C52×C11×D21)
unambiguous semidirect productC7⋊(C52×C11×C3⋊D3)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derived, HallC32×C7 ⋊ C2×C52×C11
HallC32×C52×C11 ⋊ D7
HallC52×C7×C11 ⋊ C3⋊D3
HallC32×C52×C7 ⋊ C2×C11
HallC32×C7×C11 ⋊ C2×C52
HallC32×C52 ⋊ C11×D7
HallC52×C7 ⋊ C11×C3⋊D3
HallC32×C11 ⋊ C52×D7
HallC7×C11 ⋊ C52×C3⋊D3
SylowC32 ⋊ C52×C11×D7
SylowC7 ⋊ C52×C11×C3⋊D3

Subgroups

subgroupG/H
center, hypercenterC52×C11C3⋊D21
commutator, cosocle, hypocenterC32×C7C2×C52×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C32×C7
UCSC1 ◁ C52×C11

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

9075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 319);